What model is it and how old is it? Does it do it more often or does it happen more quickly than before? If its an LCD you don't really need to worry about getting shocked by a capacitor (as you would with a CRT), but you probably couldn't do anything helpful by opening it. You'd void the warranty if its not already expired, might break something, or could have problems putting it back together EXACTLY as before and not be able to close it. As mentioned by the other post, get it replaced by HP if its still under warranty. If not, I'd look into getting a new monitor.
-mcg