Once in a while my PC fails to boot to Windows.  I get the initial screen (Compaq) but thet's as far as it gets.  I have to manually turn it off, unplug the power cable, wait about 30 sec, and then restart.  After that it boots to Windows just fine.  Anyone has any ideas?

   It has happened to me.  I just restart the computer (without waiting 30 seconds or unplugging the computer) and it works.  I figure it is just a Windows hiccup.  Whatever it is, it always seems to correct itself.  It has been a long time since it has happened to me.

If you have to unplug the computer and wait, this could be a power supply problem.
The "power supply" in the computer is actually a transformer that converts the line power to the voltages required for the computer.
This problem sounds like the core of the transformer gets saturated, not allowing correct voltages to be provided to the motherboard. "Dirty" line voltage might also cause this problem. [large variations in the power line voltage]
You might have the power supply checked to see if it needs replacement.

Thanks for the replies.  Unfortunately, it is neither of those things.  The power supply is fine, because my PC actually starts, I get the "Compaq" screen, but then it stops and does not start booting to Windows.  It sounds almost like something hangs in the BIOS.  Any thoughts?

Try your mem I had to replace a few on some computers

   Just because your computer starts up does not mean that the power supply works.  Bad power supplies often start up the computer but can put out bad voltages or stop working after a few minutes.  dlwolff0 is not saying that the computer will not start, he is saying that you are getting the wrong voltage on the motherboard at certain times which causes that.  The only way to rule out a bad power supply is to try a good one in place of your current one.
   As I understand it, this is only happening once in a while.  Is this correct?
   Have you tried just rebooting the computer without unplugging it and waiting 30 seconds?