Power Supply Failure
I can confirm with 100% certainty that this is a power supply failure. I am running Win7 32bit with a Pentium 4 3.0 GHz processor and 2GB of RAM on an older ASUS P4C800-E mother board. I am also running a SATA mirror. The power supply that failed was an ATX Switching 400W.
For a little over a month my computer would crash and restart itself (No BSOD). I thought it acted and sounded like when a transformer blows in my neighborhood and I would hear a snap from my computer before it shut down. So to me this pointed to a power supply issue as I would hear the same snap when my computer shutdown while I still had electricity.
So I ordered a new 600W ATX Switching power supply and it arrived today. As I walked into the room where my computer is I had every intention of shutting down the computer to start the power supply replacement process when I hear the familiar "SNAP' and the computer shutdown. Only this time it did not restart itself and my efforts to turn it on with the power switch were futile. I worried that the M/B had failed. As I removed the old 400W power supply I noticed the back of it (side facing the M/B inside the case) was encrusted with dust and even the internal parts of the power supply were completely encased in dust. This is because I was to lazy to put the cover back on my computer case and let it run that way for a couple of months.
I am happy to say that after installing the new 600W power supply the computer booted right up after I went into the BIOS and updated the system time settings. I got the new power supply off of Ebay from UnionPros for $24.00 shipped.