I'm not a so-called computer expert. But here's some things to look at.
Research these options first on the net before atempting them.
What is your OS... XP, win98 ... win 3.1 ...
Does it reboot in any way, or just ignores the shut down call? Can you hard shut down... turn the dang thing off at the main button? What about the alt-ctrl-del three finger salute- does that work?
(1) Can you get to your BIOS boot up screen by hitting DEL or F1..?
If you can bring up the BIOS configuration settings, look for any setting that will auto turn on or turn on by ringer/netcard incoming signal.
sometimes a wake to call/ring will activate full time if you have always on cable or such. Weirder things happen.
(2) Find 'Microsoft Systems Information', then -/TOOLS/System Information Utility/Advanced tab/advanced troubleshooting utility/and see if 'Disable fast shutdown' is checked, if so do the opposite of whatever it is, for just one reboot attempt.
Don't change anything for now, maybe report back to here... many nerds inhabit this thread...
S5