We're using ME on the computer - it was pre-installed and was bought in 2001 and in an hp. For the last few weeks, the tower won't always turn off when the shut down is done - sometimes it'll shut down okay and sometimes it won't. We've run McAfee, Ad-Aware, and Spy Sweeper and they all come up clean. We've also tried deleting the temporary Internet files, running disk cleanup, running scan disk, and running disk defragmenter. Even if we leave the computer alone for awhile after clicking shut down, it still won't shut down and we're forced to actually unplug the computer from its power source to make it (the tower) turn off and then have to wait for it to do the scan computer for errors thing when it's turned back on. Any suggestions as to what to try to fix the problem would be appreciated.

Sometimes the shutdown process gets locked up waiting for a program, which is no longer responding, to close. Try tapping the space-bar, the shift key or the return key when the system is slow to shut down.
Also press Ctl-Alt-Del and check the running processes - do an 'end task' on the more obscure ones to try to narrow down which task is failing to close. If you are shutting down you can end almost all of the tasks except explorer.
Troubleshooting shutdown problems can be a lengthy process and microsoft gives blow by blow guides for each operating system. Go to www.microsoft.com and search for shutdown Win ME.

BTW although it is best to let the scandisk complete when Windows boots, after pulling the plug, you can press 'x' to cancel the disk check and just boot.

Thanks Rimmer.