Massive Power Failure Powerbook G4 15"

Hello,

I was given a Powerbook G4 (15" 1.67ghz running on 10.4.11) by a friend who had not used it for about 6 months. The battery was not taken out during those 6 months so I expected trouble there. However, after charging it while it was switched off, it booted perfectly and ran smoothly. The problems started when I plugged in the ac adapter to charge it while running. As soon as it connected, it crashed; blue stripes and all. I have tried to charge it while it is turned on many times but it almost always crashes imediatly and sometimes stays on for a few seconds (and shows the batter connected icon) before crashes the excact same way. Also, although it charges the battery when switched-off and boots perfectly on the battery, once it is plugged in it won't come to live. It gives a little sigh and sometimes the fan goes on, but then goes silent. So I took out the battery and booted it on the ac adapter alone. It booted and worked for about an hour, and then crashed the same way. After that happened it also didn't boot from just the ac adaptor anymore.

I have tried the PMU and PRAM things, but they didn't do anything.

The adapter plug and the jack seem to be fine, they're not loose at all.

The battery specs are:

Full Charge 3637

Amperage -1488

Voltage 11387

Cycle Count 387

I guess the battery can be replaced but I wonder if that would solve the problem, knowing that it works fine on just the battery, but that it fails to boot while plugged in, or plugged in without battery. Anyone any ideas? Should I risk buying a new battery??

Your help is much appreciated!