Most likely something (like a driver or background program) causes a protection fault when XP attempts to put it in neutral for the hibernation. XP is usually set to auto-reboot for unrecoverable faults. A blue screen may come up, but too briefly to see.
To see if it is a driver problem, pull out any PCI cards, and forcibly set the video to standard VGA . Unfortunately there are also drivers for the on-board stuff, so that is an incomplete test.
See if you have any background programs running by pressing CTL-ALT-DEL and looking at "applications". Shut them down first before hibernating to see if that is the problem. Unfortunately some programs install a "service" (like hardware monitors) and figuring out what of the huge list of services (under processes) to shut down is difficult. This is the type of thing people end up doing clean installs to figure out.
FWIW, my K7S5A hibernates OK. Orignally I thought hibernating was about useless, but I kind of like hibernating when I have a lot of stuff open and want to get back to it the next day. Other than that, XP only boots a little faster. It is quieter than leaving the computer on, keeps the room cooler in summer, and saves some dollars off the electric bill.