Becaused your monitor is on doesn't mean your PC is because nowadays they mostly run off seperate plugs.
The obvious - check the back of your PC to ensure the power cable is firmly seated.
Check the fuse on your PC plug.
If no joy, remove cover from PC & ensure a green light is illuminated on your motherboard. If so, this means the power supply is OK to the PC. If not & you have checked the fuse, the 240v power unit in you PC could be defective.