Try checking the power switch connections where it plugs into the motherboard. They often can come loose when a computer is moved around seeing as they do not clip in or anything. Make sure it is securely on the pins and give it a try. If your not sure where it goes look closely on the motherboard... there is usually a very fine print labeling it.
To add onto what firekid said. Check and reseat all cable connections as any of them could come loose during the move. Also what brand is the computer. This sounds like the problem a lot of emachines T series XP machines have where when the PSU goes it takes the board with it.
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