Re-creating the problem can help to identify it. Putting it all together OK, given the information above, you should be able to figure out what is wrong and fix it. Keep in mind that only very rarely does a working Mac develop a problem that requires a visit to an authorized technician. This is a hardware problem. Either you can fix it in 5 minutes or your Mac will need service.
Some monitors show an amber light when there is no input from the computer.
Check if the Mac and monitor are plugged in. Check if there if the power is working in that outlet. If everything is plugged in and the outlet is OK, but the computer's little green light is not on, then you have a problem with the computer's power supply. Stu has a machine that gets moved around a lot and occasionally needs a hard bang on the power supply to get it properly connected. This is a classic case of an Extensions conflict.