That's a software problem. Luckily, you still have (Windows) Explorer to do just the same things as you used to do with My Computer. Consider that a useful work-around.
I am running Windows XP on a fairly new (3years) Dell computer. When I click on Start I get the usual menu, but clicking on My Computer just results in a blue screen with some sort of borders around it. I tried the My Computer desktop icon, and it worked once, but no longer works. So I have no way to get to my directories. My Documents and My Recent Documents work from the Start Menu, and I can open those files, but I can't get to the root directory listing. Is this a software or hardware problem?