Try re-seating the RAM. (Remove from sockets and reinstall) Just be sure to touch some metal (computer chassis) to remove any static.
After that, I would also run a memory test.
Here is a good one but you will have to burn the image to a blank CD.http://www.memtest86.com/
You could also remove any hardware or extra expansion cards and see if that helps.
One more thing. Many times when you get the blue screen, you will see a file name in the lower left area of the screen. If you see a filename, write it down and google it. (e.g I had a problem with ZoneAlarm after installing it on my Vista machine)
BTW, if the Blue Screen is going away too fast, boot into Safe Mode and select "Disable (Auto) restart with System Failure" or something like that. It will freeze the screen and you will then be able to write the info down.