I had thought it was the graphics card, so that has been replaced (today) and Micro Center suggested re-pasting the CPU cooling tower which I have also done.
Now it's barely getting into Windows before the shutdown occurs. I have not even been able to fully set up the graphics card yet. I let it go through the start up repair routine a couple of times. If it doesn't reboot before it's finished, it says there are no problems that it could find. The one time I got to the RAM test it finished about 80% of the full test (halfway thruough the second RAM pass) and restarted.
Any suggestions? Another Power Supply perhaps?