Ok...
Is the monitor power cable plugged in?
Is the monitor power plug switched on?
Is the monitor power cable securely plugged in to the monitor?
Is the monitor switched on?
Is the video cable securely plugged in to the monitor?
Is the video cable securely plugged in to the computer?
Is the computer power cable plugged in?
Is the computer power plug switched on?
Is the computer power cable securely plugged in to the monitor?
Is the computer switched on?
Does the computer beep at all? If so how many "long" and how many "short"?
Have the monitor settings been changed so it only appears as if nothing is on the screen? Check the brightness levels and such.
Is there someone at work who would be able to provide you with on-site or telephone support? If so, contact them, they will probably be able to provide more immediate assistance.
If none of the above solve the problem, please post back with more details, such as the make and model of the machine. As far as I'm aware RM are a "middle man" and don't actually "make" the computer, so things like the make and model of the motherboard might be useful. Also, are there any messages on the monitor, or is the machine beeping?