I've searched around and even had this problem in the past but not really found a fix. I uninstalled TS3 and WA months ago and took a long long break from my computer.. well this afternoon I installed both games, updated them and went to play and after the normal loading I get.. "Disc Authorization Failure" So I've tried the following;
The fix posted on EA's website
Uninstalling and reinstalling
Starting the game without the disc inserted to get prompted for the disc
Tried AwesomeMod.
Ran Disc Defrag, Virus Scan, unplugged everything from my computer other than the mouse and keyboard, used CCleaner.
I've uninstalled my dvd/cd rom. I really cant think of anything else to do.

I dont have any CC in my game, or mods. My games are both legit bought from Amazon the day they were released. I'm baffled, like I said I use to get this problem sometimes before, but this is ridiculous, at one point I tried over 30 times in a row to get the game working and it kept saying the same thing.

(edit)
Well while deleting cache files (trying anything here) I found this

Thu Jun 24 10:33:41 2010, DVDAUTH_RESULT_SUCCESS, D:, ( ATAPI DVDROM 16X, ALECIA-PC, Windows Vista [6.0.6002/2], DVD-ROM, ReadOnly, OTP, 2, 0x34040, 0xe85a7f, 0x22d05f, silver media, ,06000000 [1: 1077936224: 1077952593: 4210752: 0], Thu Jun 24 10:33:41 2010, 0 seconds, DVDAUTH_RESULT_FAILED_WRONG_SILVER

So yeah that looks weird.. I dont know what it means..

I've uninstalled my dvd/cd rom

How did you do that?
Can the DVD/CD drive read other disc media at this time? Music, Movies, other games discs?

Oh, and what error log is that from? or an event view log or ... ? Or how were you notified of this information?
ie what log file (if it is a file) and where is this file located?

Going into my device management and uninstalling it, restarting my computer and letting it reinstall itself. It does read other games, with no problem actually.

that log is called, DiscFailure.log and it's located in Alecia/Documents/Electronic Arts/The Sims 3

(edit)
I've got it to actually work twice now, I am bypassing the launcher and starting the game with the disc ejected and after the EA logo I insert the disc. It loaded and now after installing EA store items (that I've purchased and free items they've offered) from my purchase history it gave me some trouble, had to load the game several times using the method I got to work before it actually allowed me to play.

(edit 2)
It works but its annoying, bypassing the launcher and fiddling with the disc is really bumming me out, maybe when I go out and buy Ambitions and High End Stuff in a few days I wont have this problem. Anyway if anybody knows a better "fix" then what I'm doing now it would be much appreciated.

(edit 3; not that anybody is reading this )
It has been working for several days now with just bypassing the launcher (not fiddling with the disc anymore) I decided to download a few things (Hammond Island, and all the CC Required for it, Updated Awesome Mod, and the Daily Deal from the Sims that robs you Store) and boom, right back to disc authorization failure, even with bypassing the launcher. Tried using the launcher and still the same.

You can try a cleaning kit to ensure there are no scratches on the media and such.
If it is a problem with the disc, you have to contact EA for a replacement.
There's pretty much nothing we can do to help you out from here.

Well since getting Ambitions and HELS I've not had the problem, I honestly think it was a problem on their end conflicting with something on my computer, so new disc's no problem. thanks for the help Ellacharm3d

Thanks for posting back, and confirming closure!

But, I'd ask for a replacement disc, just the same. So that future uninstalls + reinstalls would be less frustrating, since that is the base game disc.

Happy Simming!