Close lightning hits to power lines can cause surges to all the houses in the area.
A hit close to your house can directly blow a computer from the magnetic field around the bolt.
I say this because I can't think of any reason a computer not being used would fail.
I have friend that lives on a hill, and he get hit a lot.
The last time it blew the power supply and the network card, and nothing else.
Sounds like your power supply is OK. It could just be the network card or modem, bad ones sometimes keep a computer from starting. With lightning it could be anything though.
Test all your components in another computer or try other good components in that one.computer