Shutdown hangs

My Compaq Presario laptop hangs when I try to shut it down, and it doesn't enter hibernation or standby right either. I'm running XP Home, with SP1 and SP2. Updates are current, and I have ZoneAlarm, v.5.5.094.000, and AVG antivirus, v. 7.1.371. Here are the symptoms:

SHUTDOWN -- Regardless of the method used to initiate the shutdown, and regardless of the choice of Shutdown or Restart, the shutdown window appears, but that's as far as things go. I've left it for over 15 minutes, and the fan remained on, along with the "Windows is shutting down..." screen. Eventually I depress the power button for several seconds to shut it down.

No key intervention does anything.

HIBERNATION -- Regardless of the method used to initiate hibernation (power button, Start menu, Fn/f12), the "Preparing to hibernate" screen appears and the screen goes blank, but the screen remains luminous, and the power stays on. The fan continues to run. I left it in this state while unplugged, and the battery ran down rather quickly.

The power button does not wake the machine from hibernation.

STANDBY -- same as hibernation problem.

I tried closing everything in the System Tray before shutting down, and I tried closing nearly every non-critical process before I hit one that automatically initiated a shutdown, but it still hung.

I'm at a loss for other things to try, and will appreciate any suggestions.

Bitsy