Alas. My system was in stand by mode for a long time while I was tied up on a big yard project. After a couple of days, it powered up on its own, shut down, and then just kept trying to power back up. A few times in between, it stayed on for as long as 15 minutes and I was able to do things normally until it just precipitously went off.
I thought the same thing. But replacing it didn't seem to matter.
I almost was not able to get back here to reply to your answer. My computer got stuck in a loop on this Website. It could be that I have Internet Explorer 8 now, and the site does not like it, or the beta IE8 has a bug.