Random blue screens of death (BSOD) are usually memory related,
I recommend you remove all of the memory and then try the machine with only one module installed at a time. If you have the Windows 7 installation media you can run the memory test routine from the setup menu against each module individually, and assuming no problem is found, again with all three modules installed.
If the memory checks good the next thing I would try is to replace the power supply. The capacity of the unit you have is probably adequate, but it may not be delivering rated output for some reason.