The first thing I would check off the bat is the memory and possibly the hard drive. Download and run Memtest 86+ and also a hard drive diagnostic to see if there are any errors that come up.
So the blue screen just flashes quickly then, correct? When you see it try and look to the middle of the screena nd see what kind of error it address (if it references a specific device or driver, a memory fault error, etc. that will help)
Give our Troubleshooting Procedures guide a look as well:
PC Troubleshooting Procedure List