i am pretty sure if it were shutting off due to memory you would have a blue screen and even if you diddnt get a blue screen you would get a error message afterward i think cruciallabs would be able to verify that for me.. and as long as you can keep it on run anti virus's and system diagnostic programs.. you cant go wrong most of the time you can find many for free ill try to find a few for you
edit** also what programs if any are you running to find if something is wrong with software/hardware?
intel P4 1.8
640mb sddram memory
128mb pci 5200 vid card
crappy dell mobo w/ no agp slot !