iBook G4 Strange Battery Issue

Hello,
I recently bought an iBook G4 off eBay. There is one issue with it and I am not sure what is causing it. The battery shows it has about 35 charge cycles, and when it is fully charged it says around 5-6 hours of battery life left. I will use the laptop for around an hour, at which point the battery life is at around 80% with around 3-4 hours remaining. All of a sudden, the computer will go into sleep mode and when I plug the charger in, the battery is at 0% and charging! I am not sure if this is a bad battery that is old and can't hold a charge, or what. I have already tried resetting the PRAM and PMU but with no luck.

Any help would be appreciated.

Thanks,
robbier

Under full charge capacity, it says "6991 mAh."

I am not sure if that is good or bad. However, I still do not understand how in the world my battery would be at 80% with a few hours remaining and then all of a sudden go into sleep mode and have 0% of a charge left.

Thanks again,
robbier

I am fairly certain that it is an original Apple battery, it has the Apple logo on the back as well as the model number "A1008." It looks authentic and original.

Thanks for the help. I am not sure if this matters, but would using a 3rd party replacement charger/AC adapter make any difference? The charger is compatible with the iBook.

Also, does it matter which brand of replacement battery I get? I can find one for around 40 dollars on Amazon, but I don't know if it matters if I get the more expensive ones.

Ok, here is some new information I just discovered: When charging the laptop, it charges slowly up to 20%, then immediately goes up to 100% like its fully charged. Does this sound like a bad battery? If so, does it matter if I buy a cheaper replacement battery, or will it be of bad quality?

Here is one I am thinking about: http://www.amazon.com/Battery-Apple-ibook-Laptop-A1008/dp/B001RDBDJG

Thanks again,
robbier