Unplug the system from the surge protector and plug it directly into the wall outlet. Could be the protector took a 'hit' and isn't functioning anymore or just barely.
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If it still doesn't power up, can you count the buzzing sounds? One long one indicates a RAM stick that may have come loose and just needs to have the case opened up, pull the stick out and reseat it firmly.
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If it still doesn't boot up, and there are three buzzes, it could be a video card gone bad. If it's on-board video, you will have to open the case to see if you have an AGP slot available for a separate video card that you can install, then go into the bios and disable the on-board video. If you have only white PCI slots available, that's the type of card you will need to buy.
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If it still doesn't boot up, while the case is open, try to power up and see if ALL of the fans, including the one for the power supply are moving freely...if not, get a can of compressed air and clean them all out and try again...one of the fans could be stuck on debris and not moving at all. You can either remove the fan and clean it with a cotton swab and rubbing alcohol or replace it.
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If the system isn't powering up at all, consider replacing your power in case it also took a hit or just died a natural death. If you have to replace the power supply, look carefully at the pins for the front of the case as you remove them and mark how the new one will have to be hooked up later.