Kinda sounds like it could be a power supply issue, like one of the capacitors is going bad in there maybe, do you have a different one you could try? Does it try to start at all, do any of the case fans or power supply fans spin when you attempt to start it? Have you tried leaving the power strip over night, does it start then? Some system specs could help, how old is the PC? Have you tried plugging the PC directly into the wall outlet, could be the power strip? When you get it running look at the event log to see if the PC logs an event when you try to start it. I'm pretty much just shooting in the dark till you post some system specs and try some of the troubleshooting I suggested.
Just my 2 cents do with it what you will.