most hardware stores can probably provide you an alternative switch device.... just be careful, as always. you might be able to cross the wires to turn on the computer and put it into target disk mode to get your data off...
also, I don't know if this makes sense to you, but I think the wires only need contact, and don't need to be together the whole time the computer is one (it's just a button, not a switch. so you can probably just cross the wires for a quick second to turn it on. BTW, one of the wires is a ground most likely.