why won't my Sony PSP turn on?

I've had it for about 2 years, i'm not sure what model it is, and it stopped working a few days ago.

two weeks ago, one of the batteries that i have for it started leaking acid out of the protrusion that plugs into the device, so i stopped using it. as far as i can tell, the acid didn't do any damage to the actual device, but now it just doesn't turn on.

when i hit the power switch, the light flashes green for a few seconds, then goes dead. and when i plug the PSP into the charger, the orange charging light comes on, but i get the same result when i hit the power switch. even with the battery out and the charger in, the device does not turn on.

what could be the problem?

what can i do to solve it, or will i have to buy a replacement?