The short answer to that is no, but the long answer is "sort of".
The PC contains an x86 processor but the PS3 contains a PowerPC-based processor. So, the PS3 cannot run Windows games, nor can it run pre-compiled games for Linux that are made for the x86 platform. It can run games compiled for the PowerPC platform. If you can obtain the source code to a particular game, you can compile it yourself and run it on the PS3. But, there is a caveat - the PS3 does not support any hardware acceleration through Linux. So, any game that you run through it will have to be done in software rendering which doesn't look as good, and is significantly slower (we're talking even Quake 3 having difficulty running in software mode).
If you really want to play PC games, your best bet would be to buy a new PC.