I'm stumped with the Wifi/router being part of shut down issue and that connects into the modem... so maybe the router or the modem??

maybe something to test ?? - If you can do a test by plugging in with a cable -temporarily to the modem only , and not use the router at all - to see if the normal shut down works that way - that would most likely point to a router problem.

and if it has the same shut down problem then a closer look at some heavy duty scanners and maybe doing a "hijack this" log.
http://free.antivirus.com/hijackthis/

but hopefully mrsD's son has tips for the running processes investigation.

but some trojans can make the computers do weird things like stay online and restart...


My set up is phone jack to modem to D link wireless router & the signal goes out to wifi card in the
computers.