The hard drive isn't the probably, and generally, your BIOS will not be happy if their is no hard drive, and I could be wrong, but I always thought live linux distros needed a hard drive, I could be wrong though.
It looks as though either their is something wrong with the RAM modules, or the motherboard itself. Go on Google and search for Memtest86, it's diagnostic program that you burn onto cd and boot up the system into, just as you would with a Live Linux. Then you can run various tests for your memory, since this is a Linux forum and their are many resources out their to help you figure out Memtest, I won't go into the details, but I'm sure you'll find it's not to difficult to run.
Let us know if that helps in finding the root of your problems.