Have you tried turning everything (monitor and PC) off then turning it back on?
Also, after computer is off, also turn the PSU switch on back of CPU off then on.
Are display and PC connected to the same power saver?
After doing above, when you turn on computer, do you see any lights or hear any sounds? What?
Since display apparently turns on it sounds like you have power to the wall socket and power saver.
I once had a dead computer and spent 30 frustrating minutes trying to find the problem. I checked connections inside and out of the computer - several times, traced back to the power saver and wall (which required moving my computer and a desk to squeeze in back where the power supply was). Plugged it first into a different outlet on power saver and then, even tho power light was on the power saver, directly into another wall outlet. Still dead. As I retraced my troubleshooting mentally, I looked at the back of the case - now visible since I had pulled it out from under desk - and observed the power supply switch on the bag. Since I never use it, I never thought about it. But somehow it had been turned off. I simply turned my PC power back on and was back in business.