OK, a few more Q's. Which operating system, Win 98, 98SE, 2000, ME or XP?
Is it connected to a network at all, or anything else "external".
It's possible that there is a problem with Norton, I've had some "issues" with it in recent times where it does not completely close clean on shutdown. On XP, the machine sorts itself out, but on 98, that can very easily end up with it on the "the machine is shutting down" screen for ever. What's happened is that 98 has said to a driver (that's an internal programme routine that makes the machine do something specific with a program or piece of hardware) "please close", and for some reason, it's not seen the reply correctly, so 98 sits there for ever waiting for a reply that's it's gone, which it never gets.
There are other possibilities. Has this started happening recently, and have there been any changes to the machine around the same time (maybe a USB printer added, or software for a digital camera added, things like that) or have you installed any new software recently.
Sorry if this seems a little vague at the moment, it's going to take a little while to narrow down the area of hassle before we can try to nail specific things more accurately. Even then, it might be luck, with some versions, there are know problems with shut down that never got completely cleaned up. All we can do for now is try and narrow it down a little.
Cheers