Zing

do you have a blank cd? if so download the pre compiled memtest iso I linked to and burn the iso image to cd using imgburn( freely available) Then you will need to boot the pc from this cd

When the PC boots you will either see a full screen menu or a series of messages. IF you see a full screen menu hit the tab key and this should show you the messages

You are looking for to enter set up hit F2 or Del( most likely one of the 2) or better still Boot select menu hit F8 or F12( again normally one of these) if there is no Boot select menu then you will need to enter bios set up and set the cd rom as first boot device( you never know with a bit of luck it may already be set to this so boot with cd in first and see if it loads)

Prime95 freezing makes me think bad stick of ram as if it was a cpu fault it would fall over on a bad calculation and tell you. It could of course still be anything as kymmy says a failing psu or mobo could result in the same error

I would not trust the Windows Diagnostics as a deffinative answer but did the system crash after you set a static page file ?