|Here is what to do to troubleshoot the problem,|
1) Check the cable between the monitor and the computers graphics card - make sure the connection is nice and firm.
2) Try another cable - could be that the cables pins are damaged.
3) Try the monitor on another computer to ensure that the monitor isnt broken.
4) Open the PC case and check that the graphics card (the card to which the cable attaches to) is firmly in place and not come out of the slot - might be an idea to take it out and replace it.
5) Power Supply it could possibly be that your PSU is failing and not able to supply enough power to boot the machine. If you have another, swap it and test.
Note - when opening the machine ensure you remove all power from the unit to avoid hurting yourself and damaging the components in the machine.
let us know what happens.