Welcome to Tom's Hardware Forums,
There are quite a few possible reasons, because of the age, I will suggest replacement of the CMOS battery (little watch battery on the motherboard) as a first course of action - not expensive, can be purchased at your local watch/hearing aid battery retailer.
Your power supply may be dead at this time also as OEM PSU's aren't really designed to last more than four or five years, anything over that, you're doing good. I can go over your options there but I would do the CMOS battery first.
Good luck
Afterthought: At the back of your computer there are four led's - are any of them lit when you attempt to power on?