If you run across a computer which has been asleep for a long time, that is, it perhaps sat in storage for months or years, expect nothing to work correctly at first. The power supply, and the monitor, as well as many of the cards and perhaps the mother board use electrolytic capacitors which degrade when they are not being operated at the expected voltage.
Larger electrolytics, which you might find in power supplies, UPS systems, and on the boards of monitors, are especially prone to this sort of sleeping sickness.
What to do? Just plug it in, turn it on, and let it sit for a day. If the equipment doesn't immediately go up in smoke or blow fuses, the capacitors will reform over a period of time. If the equipment still doesn't work after a day of being plugged in, go figure something else.