What kind of monitor?
What kind of PC?
It could be it isn't the monitor at all. Are you sure the PC is starting up properly?
Can you hear beeps from the PC? Are they the same beeps each time it starts up and the monitor doesn't come on?
When you are powering up the PC has it been off for a while before you restart?
Check your video card is properly seated.
Poorly seated memory can also cause a computer to hang.
Try turning on the monitor first and then turning on the PC. Do you see the start up information? If so, and then blank when the OS starts up, then it isn't the monitor but an issue with the PC hardware or software.
Unplug the computer. Open the computer, blow out all the dust. (Don't use a vacuum as that can cause static electricity and fry your computer) Ground yourself by touching the metal case then push down on everything that is in a slot on the computer. PCI cards and memory. If you feel comfortable doing it, you can remove the cards and put them back in.