I had a user say that to me one time.
The power cord had come loose in the back of the monitor. Pushing it back in was all that was necessary for me to fix it and for me to make the user feel like a retard.
That being said, that is only one possible cause out of many as previous posters have stated.
Ideally, it would be nice if you could get us full system specs including maker, model, and approximate age of every major part (motherboard, processor, ram, video card, monitor, hard drives, etc).
Also, it would be nice if you could get us the settings for power save modes that are present on the computer.
The first thing that you should try almost without question is to switch out the PSU for a known good PSU. If there is another computer in the same office of the same kind that works, try the PSU from that computer in the one that doesn't work.
Almost without exception when a computer starts to age it is pretty much always the PSU that is the first thing to fail. This can cause problems such as the inability to leave standby mode (the +5 SB power cable working outside specifications, for instance).