Leo says It could be a mechanical failure like a shorted on/off button that keeps turning itself back on. If that were the case, however, hibernate wouldn't work properly and Lisa says it does. It's possible that in the BIOS settings, "wake on LAN" is enabled. She should reboot her computer and press the 'f8' or 'esc' key and look in the BIOS settings for "wake on LAN." If it's enabled, disable it.
If she can shut down in safe mode, then that would mean that something is running that is causing it to reboot. It isn't the end of the world if the computer won't shut down though either. If she can hibernate it, that's just as good.
Another thing is that Windows may be installing updates because she hasn't had it online in quite awhile. So it may be updating and when it's done, it may just shut down after that.