PC shutting down during W7 install

Hey guys.

I'm having a bit of trouble installing Windows 7. Whenever I get to the "Expanding Windows files" portion of the install, my PC will just shut down. The shut down isn't at a consistent place either, which tells me it isn't the disc (which I burnt a W7 iso on to). It'll shut down at about any percentage through this portion of the install. It's shut down at 6%, 55%, 95%, so not at any one point.

My PC isn't new by any means but it should be able to run 7.

My specs:

AMD 1.61 GHz single-core processor (yuck, I know)
2 GB DDR RAM
Dual nVidia 256 mb 8600's
120 GB HDD

It was built about 4 years ago, so it's not a new, untested build.

Any help would be appreciated.

Thanks,
Cal