ugh... you're not going to like this but this is a common problem with these iBooks. The only sure fire way to fix is to replace the entire logic board which is not cheap. Your best bet is to send it in to powerbookmedic (or at least email them to see what they say about it) or find a logic board on eBay and do it yourself with a take apart manual. It's not impossible, but it's not fun either!
Unfortunately, this issue is not covered under Apple's logic board replacment program, but it's worth a look to see if you have any of the other issues listed here: