I recently tried running some semi-modern games on an old AMD machine with an Athlon II x3 Rana CPU. It was terrible. Since the only triple-core processors AMD made were from that same era, I expect most others will be about the same.
Yes, you can unlock the fourth core SOMETIMES, but it's not always stable. I did that with the above-mentioned machine, and it picked up the annoying habit of crashing randomly during boot most of the time. Turning that core back off solved the problem.
Probably the best you're going to do for $30 is an old LGA775 quad-core, say the Q9400 or Q9550, and then overclock the hell out of it. But then you're still only going to get mid-low tier performance out of it, and you're stuck on an 8-year-old architecture that's obsolete by three generations. If you want to do any serious gaming, you're going to have to do better than that and up the budget a little.