I suggest disconnecting all leads from any floppy/hard/cd drives and removing any modems etc from the PCI slots.
Connect to a monitor and try switching it on.
If nothing happens at all (ie it doesn't switch on/make any noise), it is highly likely that it is the PSU that is the problem.
If you have another PC that you are able to remove the PSU from and try in this machine, this is an option and will allow you to see whether or not this is in fact that faulty component.
The other possibility is that the motherboard battery is dead, in which case you can either buy a new one or buy a new motherboard.
Hope this helps
Matt