Sounds like either a hard drive that is failing or maybe the memory (RAM). If you know what brand hard drive, you can get some diagnostic software from the company (usually free) and test the HD. You will either need to have a floppy or possible it'll allow you to create a cd, from a working computer
you can download a memory testing program here
http://www.memtest.org/. Again, you can either make a floppy or CD. They are self booting.
Dave