If you research "XP WON'T SHUTDOWN" you discover thousands of posts and maybe 10 times that advice on a cure.
Since this sounds like the usual problem we rarely try to fix it today as the clients don't want to pay for OS REPAIR so we backup what files they want to save then reinstall the OS. If that doesn't cure (does better than 1/2 the time) then it's the hardware and given the age of the PC, few fix that.
I have a Dell Dimension DIME521, Windows XP, Media Ctn. Edition, Version 2002, AMD Athon (tm) 64x2 dual core processor 3800+, 1.00 GHz, 960 MB ram. My problem is the computer will not power up after sleeping or hibernating so you have to power down by holding in power button on tower and pressing again to start back up. This started about a year ago but has gotten worse over time. At first after cleaning up/deleting files and defraging this would take care of it for a while but now doesn't seem to help much. At first the time frame of being able to wake it up was longer but now you have about 30 minutes maybe before you have to power down tower and restart. I've been told to power down on the tower is not good. How long will the system take this? We currently have DSL @ 768/256 but it seems slower than that. Any help would be appreciated.