you can change the behavior of the pc when it blue screens by pressing F8 at boot and selecting "Do not restart" on errors, or something like that. It will give you time to read the error messages. From the information you have so far, it sounds like a bad stick of ram, or incompatible ram. Please post your system specs with model numbers of your components.
You can try running memtest by choosing the option when you press F8 at boot, also.