I booted up with Linux and it kept running.
I booted up in safemode and it kept running.
I ran memtest 4 and found nothing wrong.  
I ran Kaspersky antiviurs from a boot CD and found nothing. It ran this for at least an hour.

I booted the computer when it came and started to look for something in Google and it shut down, click.  I pushed the power button to restart but it didn't run.  No lights were visible and monitor was just flashing the power button.  
I held the computer power button down for 10 seconds.  Then pushed it and the computer booted just fine.  I then ran msconfig and set it to boot into safe mode.  In safe mode I surfed the net without incident.  

Currently I'm checking the hard drive for errors.

I did blow out the dust from the computer.