iBook - clamshell power problems

Hi everyone, I'm a noob here.
I've got a problem with an old clamshell ibook that doesn't seem to be very common as I can't find any solutions to it on the web.
I bought it off ebay a while ago and after a few weeks it went dead and refused to boot. It wasn't even running off mains or recognising that there was a mains charger plugged in. I was very pessimistic about fixing it but i bought a new battery anyway as a last resort, put it in and viola, it worked. I have only used it intermittently over the space of about 5 months, and already the battery has died and I have the same problem as before (won't run off mains, won't even recognise mains is plugged in). I am suspecting that if I buy a new battery it will work again as before, but I am eager to fix the problem that is preventing me from running of mains when the battery is dead and that is potentially(?) causing the battery to run down so quickly. Could anyone enlighten me as to what could be wrong?
Thanks,
Laura