Smells a little like a dodgy RAM chip possibly. If you have two banks of RAM take one of them out and run on reduced RAM to see what happens. Then swap it out, to try and verify performance against both RAM and the sockets, too.
While you are at it, after having earthed yourself against the PSU (do leave it plugged in !!) just lightly press chips into sockets in case thermal creep has dislodged something or other over time. Also, disconnect and reconnect any leads, to check if there is an intermittent connection.
It might not be any of this, but I have seen similar situations to this more than once and it is not a bad place to start the detective work if it is a hardware fault.
Do let us know how you are carrying on.
Good luck,
Conan