Several very broad guesses:

Have you recently uninstalled any EPs?

Have you recently downloaded and installed any complete custom Sims? If so, they may have come with something which is in conflict with what you already had.

If you have any default replacement skintones in Downloads, try temporarily removing those and see if the problem clears up.

Ditto if you have a default replacement CAS file.

Run Clean Installer and check for duplicate files. Hint: clicking the MD5 tab in Clean Installer after it has scanned and loaded all your Downloads files will group duplicates together (they're highlighted in pink), so you can more easily run through the listing and remove all but one of them in each case.

If you've downloaded and installed any bed or woohoo hacks or any custom bedding, would start by testing the game with those removed first (don't Save the game, just go in and see if the Mission bed is working for you).

If those aren't the culprits best bet is the tedious, but tried and true, 50% method:

http://www.sims2wiki.info/wiki.php?title=Game_Help:Finding_Problem_Custom_Content#The_50.25_Method

Pardon the question, but -- are you sure about your disk drive?

You say "new computer" -- are you sure your disk drive is a CD-only drive rather than a CD read/write and DVD read-only drive?

The vast, vast majority of contemporary disk drives include an ability to play DVDs, but not record or write DVDs.

DVD read capability is all you need for your Sims discs.

Without having University installed, you probably can't get or use an actual resurrect-o-nomitron. It was introduced as both a career reward object in University and as an in-house object at colleges' Secret Society. There are buyable versions out there too, but so far as I'm aware they also require University be installed.

However, you can resurrect dead Sims (with or without University) using Insimenator or it's Mortality Adjuster.

Documentation on that adjuster (it is a part of the whole Insimenator and not available solely as a separate object) here:

http://www.insimenator.org/showthread.php?t=605

Strongly recommend getting all patches.

Unpatched games can generate all sorts of little glitches, malformed interactions, wonky Sim memories, things just missed (or which never came up) during beta play testing, etc. Over time, the accumulation of glitches within the history of the gameworld may impact the entire game negatively. Too, there exists the possibility of some custom content not performing as expected or completely as intended in an unpatched environment.

Would that any complex interactive software (not just Sims 2) came fully and functionally perfect out of the box on first release. But that just ain't the nature of the beast.

If a graphics option is grayed out, usually means that it is an option which the game has determined your video card cannot handle, or one which if enabled might cause damage to your video card.

3 questions:

1) Have you installed all the patches for the game and for each EP and SP?
Patches should ideally be installed in the same order as you installed the EPs and SPs.

2) What video card is installed on your computer?
If it a card on the low-end of the 'suitable for Sims 2' list, it just may not be capable of handling some of the additional more intensive graphics requirements of the later EPs.
A new machine may or may not have installed at inception a perfectly adequate but not necessarily robust video card geared towards gameplay.

3) As it a new machine, are you running Vista on it?
If so, is it a dual core or quad core system?
Sims2 and all its packs are designed for single core systems, but there is a way to set things up on dual or quad core systems to get around that.

First, it's not a recommended procedure, as it carries the potential, if not done 'just so,' to break the 'hood and/or the game (if not immediately, then later on down the line).

That said, the tutorial for doing so is here:

http://www.sims2wiki.info/wiki.php?title=Game_Help:Moving_Sims

Try it as written at the link Auronette gave, including the caps:

boolprop allow45DegreeAngleOfRotation true

Should work so long as you have at least one EP installed. If only playing base game, you cannot use this cheat.

Some computer/game systems will accept cheats without caps -- all computer/game systems will accept cheats with the caps.

You can permanently include this cheat in the game by putting this cheat into your userstartup.cheat file. See here:

http://www.sims2wiki.info/wiki.php?title=Game_Help:Userstartup.cheat

Use the Insimenator or  the Temporal Adjuster object which is a part of the Insimenator to change her to any age at any time.

http://www.insimenator.net/forumdisplay.php?f=38

One caveat, though - if reverting a Sim to a baby, best to also make that reverted Sim then unselectable, as having babies being selectable Sims and then Saving the game can possibly cause game problems in some instances.

Apologies if this is too elementary, but are you putting the rar file into Downloads? It doesn't go there.

For custom content (that is, other than Lots or Neighborhood Terrains) the contents of the rar file need to be extracted, and then the package files put into your Downloads folder.

Personal choice for both unzipping and unraring is 7-zip (free, safe and user-friendly):

http://www.7-zip.org/

or you can use Winzip for zip file extraction and Winrar for rar file extraction, or another extraction program of your choice.

See here for a bit more:

http://www.insimenator.org/showthread.php?p=1418051#post1418051

As for fixing the thumbnails, you can try this:

Go into My Documents--EA Games--The Sims2 folder.

Delete the groups. cache file (the game will auto-generate a new one for you when you play).

Then open the Thumbnails folder and delete all the contents inside it, but not the folder itself (the game will generate new thumbnails for you as you browse through the Buy and Build catalogs).

Your game may load slower than normally for you only the first time you launch it after the above deletions.

Most likely you have a previously installed buyable mailbox or else a previously installed mailbox hack. Those need to be found and removed, and then the problem should resolve itself.

Additionally (and totally optionallY) you can afterwards choose to install an Apartment Life-compatible buyable mailbox:

http://daydream.etowns.net/

The only way I'm aware of is to use the Lot Adjuster (successor to the Lot Expander) mod:

http://www.modthesims2.com/showthread.php?t=282409

to expand the lot, complete all the building, then shrink the lot.

It's a little complex to use.  Do definitely take the time to read through and learn the tutorial first, as this mod potentially can really play hob with your game:

http://www.modthesims2.com/showpost.php?p=1773743&postcount=410

Take a look here for a tiny bit of how-to in addition to the LotExpander tutorial:

http://hideki.modthesims2.com/showthread.php?p=1802193#post1802193

Before getting into back-ups, here's the link to all the patches:

http://thesims2.ea.com/update/?pid=Help_patches

You should probably do a quick run-though of the wiki's section on back-ups:

http://www.sims2wiki.info/wiki.php?title=Game_Help:Back_Ups

but here's a really condensed version:

Open My Documents--EA Games.

Right-click on The Sims 2 folder.

Choose Copy (or if Copy is not an option in the right-click menu, use either Control-C  or Edit--Copy to copy the folder and all of its contents).

If, during the copy, you get an alert box asking if you are sure you want to copy something, click 'Yes To All.'

Go back to My Documents and create a new folder (you can name it whatever you wish) and open that newly-made folder.

Click inside that folder to 'set' the cursor, the either click Edit--Paste or use Control-V to paste the copy of the entire The Sims 2 folder.

This will take some time to finish, dependent on how large your copied folder is - it can certainly take a half-hour or more in some cases.

If, during the paste, you get an alert box asking if you are sure you want to paste something, click 'Yes To All.'

Once done, you'll have a copy of the pre-BV folder and can use that copy to replace a damaged or corrupted folder should that ever occur AND should you later decide to uninstall BV - the copy, if used as a replacement, will pick up the game exactly where it was when you did the back-up; that is one reason why periodic back-ups are recommended, to keep them current with your gameplay.

If you are happy with BV after it is installed and you've played it, I'd also recommend doing a separate fresh back-up of the BV-impacted The Sims 2 file to have on hand in case your with-BV game goes phffft at any time.

First thing to do before installing anything is to do a back-up of your complete My Documents--EA Games--The Sims 2 folder, just in case (if you experience problems and later want to uninstall BV, you'll have a non-changed pre-BV back-up to replace the BV-impacted The Sims 2 file).

After that, you should be able to go ahead and install BV.

It doesn't matter to install earlier EPs.

After installing (and before playing), be sure to get and install the BV patch.

As far as using the game, you'll always have to start it from the most recently released EP (as opposed to only the most newly installed), so that should not change for you.

Not a solution for the particular clothes you are having problems with, but perhaps a help for the money situation.

You can use this hang-on-the-wall hacked dresser to shop for outfits for free:

http://www.modthesims2.com/showthread.php?t=225251

Or you can use the family funds cheat to add back in specific money amounts which have seemingly gone off into neverland:

familyFunds familyname amount

For example:

familyFunds Smith +94

will add 94 simoleans to the Smith family's total.

The familyFunds cheat, IIRC, requires you have Nightlife installed.