My PC has a 7770, Phenom II X4 and a crummy old DDR2 motherboard, runs games fine. Only thing that annoys me about it is fan noise- might be tempted to replace the GPU with a quieter card, but that's it. Don't see the need to spend a fortune to play the games I like when I can just turn the settings down slightly.
Specs at 800x600 then? Define "fine".