2) Why would I need the base game installed when it says on the back of the box that it contains The Sims 2, Nightlife, and Celebration Stuff
You wouldn't. Was asking because, if it happened that you had it installed, that would cause the problem you describe, as the base game would need to be uninstalled if trying to run Double Deluxe.
Forgot one more question: is Double Deluxe all you have installed or do you have any other EPs or SPs also installed (Uni, Seasons, Pets, etc.).
The game needs to be run from whatever the newest-released-by-EA/Maxis EP is (or in some cases the newest released SP).
For example, if you had just Double Deluxe and also Open For Business installed, you would need to use the OFB disk, not the Double Deluxe disk in order to play as, even though Double Deluxe came out for sale after OFB, OFB remains a later original release than either of the EPs (base game and Nightlife) included with Double Deluxe.
Next step would be to carefully clean the disk to make sure there aren't any tiny gobs of gunk on it (even brand new disks are often better served by a thorough cleaning).
Also, when prompted to install the disk, when you click OK, what happens? Does it sound as if your disk drive is starting up (may take a short while for that to happen).