This happened to me once;
I borrowed a PC from a fiend. I tried installing Windows XP on it, but it failed (the installer was freezing). I only managed to get Windows 2000 installed. And when I was trying to install a program, 3 of 4 times I got an error message and setup was shutting down. I also installed some games on that computer. Only half worked and those half where closing for no reason when I was in the middle of the game.
I spent some time making settings in BIOS and thinking. I never managed to figure out what was wrong, until I putted the RAM from this computer in mine and... BANG! It crashed.
So, if you have the same problem or something similar, it's surely the RAM's fault. Try to buy new RAM because if the test fails once, there's surely something wrong.