Thanks for all the valuable posts - which I've read and benefited from on the sidelines, until now.
I have a 4-or-so-year-old Lenovo desktop (IdeaCentre K210), which I generally love. It's a 32-bit system so I'm running at the maximum 4GB RAM, and recently upgraded from Vista to 8 (would have loved 7 but 8 was cheaper). Everything seems to be working pretty much normally.
EXCEPT - "normal" on this computer has always meant that there was one thing I can't do... reboot. I can shut down completely, and turn the power back on, no problem. When I click "Restart" on the power menu, however, it does what it's always done - it enters a loop where it tries to reboot from 1 to 3 times - the fans boost up like they do when I start cold, I see the BIOS stuff, and then, instead of seeing it enter into the OS, it blacks out, and does this process again. Eventually (like I said, after 1 to 3 cycles), it stops trying, and I see a black screen with a single flashing cursor on the upper left hand corner of the screen. If I then manually turn the computer off (this is using the button, now), and start back up after a few seconds, it solves the problem. This applies to things like Windows Update as well - if it tries to restart, which it always does after the more significant updates, it enters this loop; I then perform the same power-off-power-on procedure and it completes the updates and life proceeds as normal.
I've tried to update the BIOS - figuring that this is the problem since I've done a number of completely clean Windows installs and on different OSs at that - but the utility Lenovo provides for this system doesn't seem to work... although I am trying the version of it as a windows .exe file and not a manual BIOS flash (partly because there seems to be no utility available from Lenovo or functionality within the available utility for backing up my current BIOS), and that exe may be for an earlier version of Windows.
Anyway, any insight you have would be much appreciated - this is not a debilitating issue; in all other regards this system continues to perform quite admirably. It would be nice, though, if it could "restart" - particularly for things like automatic updating.