DarinBad
If you haven't done so already (didn't see it mentioned in the thread), you could try re-seating the memory, video card, cables, etc.. Even though the computer may boot up initially, connections may move around due to heat expansion after things warm up. A friend of mine had exactly the problem you describe a few years ago. I re-seated everything, and the problem was gone.
A failing power supply could certainly cause this also.
Yes I agree this is wise to do, I am going to disconnect all devices, and open the case for cleaning and check all the connections and generally see if I can see anything. Then see if I can boot with all audio components disconnected. Next I'll try a new power supply. But before either, I am going to run a driver utility in safe mode and perform chkdisk as mentioned above.
I really appreciate all the help on this and advice you all have given, I, myself, would not have been able to go to these lengths with my own knowledge.
I should note, the blue screen came on the hottest day of the year (rare for fall, but we had a three months with no sun and only rain for our summer, on the average 3 days / month without rain, now in the fall our summer has arrived!). Although my room is closed up and rather steady in heat, humidity, it does cause me to think of overheating.