MacBook shuts down when releasing power button

This is hard to explain so I will try my best. I unplugged my MacBook pro to move it to another outlet, I then tried to power it on and it wouldn't turn on. My batter doesn't hold a charge so I keep my computer always on the charger. The charger light is green and when I hit the power button the computer doesn't respond, when I hold the power button it starts making booting noises and then shuts down as it would of someone holds the power button down for a hard shutdown. I tried unplugging it from the charger, removing the battery and holding the power button for five seconds. Still doesn't work, any help?!?! It's a 2008 MacBook pro

I would say you need to replace the battery. Any reason why you haven't tried doing that? Other World Computing sells replacement batteries that exceed the Apple specs.