shutdown problem in Win Me

I have a computer here that has Windows Millennium Edition on it and although this is a reasonably modern system, all windows updates are fine, anti virus up to date drivers are fine, no installation conflicts, the hard disk drive has plenty of freespace on it, all PCI cards are frimly seated as is the ram chips.

The problem is that most times when the computer is shut down, it hangs during shutdown and the message It Is now safe to turn off your computer message does not appear. There is just a black screen and the computer is still running.

Anyone got a solution to this problem?