sounds like either PSU or MOBO / RAM
easy way to test if you dont feel like waiting on memtest,
load up your BIOs set your ram to the slowest setting your BIOS has so if your running DDR2 800 drop it to DDR2 667 or 533 etc if that fixes it well your memory isnt stable anymore

and means you should run a memtest on each stick at its actual speed and see how they do, when done test 1 stick of ram in each DIMM see if its a particular DIMM thats gone faulty
also agree with total headache check temps just to err on the side of caution
could be age aka Motherboards are now manufacturered to fail after 3 years if your system is older then that well your system has lived past its expected life span its done this way to keep people purchasing products, but i doubt this
everyones already stated the obvious
memtest , check dimms, lower Ram speed test for stability,
check temps
test with a different PSU,