$500 will be touch with an I3; don't forget to factor in ram, disk, monitor, case and psu. Not sure what to suggest; to be honest at the $500 price point you might be better off with a dell or hp. You will need an I3 if you go with a decent GPU. The thing is that these prebuilt systems can be a bit cheaper than the individual components if you build your own system; where they suffer is high end customization but $500 is not going to get you a high end system. Now if you want to a system limited to the processor GPU you can build a decent system for under $500; esp with the Petinum you can build something nice for $350 - esp with if you go with ddr3; but those system aren't really game system. They can play some older games - esp rpg - that are not graphic intensive.
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Perhaps you should give a better description of what you consider a 'gaming pc'.