GeForce 660 TI Imcompatible with Asus 6830-07?

Check all the plugs, connections, etc.
You might either have to update the motherboard's BIOS, or replace the board completely (which would also entail a replacement of the CPU if the socket in a new one is different)

That PC comes with a 350w powersupply, that WILL NOT POWER that card. You NEED at least a 500w to 750w power supply.

Anytime you buy a computer from bestbuy, office depot, etc and you want to upgrade the graphics card, you almost always have to change the powersupply.

My recommendation is probably a 600-650watt powersupply. Its right in the middle so price shouldnt be too bad.