Turning off a computer (or pretty much any electrical device) does not protect it from power anomalies during a storm. Computers in particular are still very susceptible to surges and spike and other anomalies because when the computer is shutdown, it is still in standby mode and the power supply is still providing +5Vsb standby voltage to several points on the motherboard.
The only true way to protect an electrical device during a storm is to unplug it from the wall. The next best way is to use a "good" UPS with AVR, and lastly, use a surge and spike protector. Of course, nothing can protect you from a direct lightning strike - not even unplugging - if the bolt is
determined to get you!
Since you tried another monitor/TV and have the same results, you need to swap in another known good power supply and go from there. If you don't have or cannot borrow another PSU from another working computer, you need to have that PSU tested by a professional to make sure it is supply all the necessary voltages. Unless you have a decent oscilloscope or a true power supply analyzer (and know how to use them and interpret their results), the only way a "normal" user can verify a PSU is working properly is to swap it out with a known good supply.
You might also try that monitor on another computer
Edited by hamluis, 19 June 2016 - 01:28 PM.