So you've been having this issue with Sims discs? Not just starting with Pets?
Since it is a new iMac, I'd call Apple care. Like I mentioned, there's a faulty "something" with their disc drives. I don't know if it is hardware, or firmware or loose soldering or what. Some have resorted to using external DVD players.
There's an FAQ I read (although I cannot locate the link on EA's site now anymore, but the threads below has the gist of its contents) that disabling Time Machine sometimes help. As does ejecting any peripherals that has a harddrive, eg iPod, iPhone, USB thumb drives, etc. Or if you have any Disc burning software, to make sure that is not running in the background while playing Sims.
You've tried restarting, yes?
Why wait until you get to a store?
Doesn't the Apple Care you pay for (that cost a bomb) entitle you to support via telephone? I say use all the services at your disposal. They are all paid for after all, let them work for it.
I used to have that problem too. In the folder "Downloads", there's a file called "tslus.bin". The first time I downloaded custom content(.sims3pack to the "Downloads"-folder), it automatically moved to another folder(the main folder, The Sims 3). You just have to move it to the "Downloads"-folder again and it should work.