My 3 computers are having problems, they all turn off and on by themselves. What could be the problem?

I have 2 desktops(more than 5yrs old) and one notebook(1 yr old) all three of them are turning on and off by themselves. Could it be some sort of virus? I've scanned them all with avast, McAfee, Windows One Care but they haven't found anything suspicious. Also could the virus/problem be coming from the modem?