Battery, charger, or DC in board defective?

My 14" i-Book G4 1.33 GHz will function fine with the A/C adapter attached, but the battery will not charge. I had to buy an different adapter from the one that came with the machine (on eBay), and it does not have the colored lights on the barrel connector, so I can't tell if it's charging. The adapter is marked "Macintosh PowerBook ibook 45W AC Adapter"and says it was from Apple Computer in Cupertino. It gets hot, so it's getting current, and the battery icon on the machine shows that it's plugged in, but the battery charge remains at 61% regardless of whether the computer is on or has been turned off for awhile. When I disconnected the charger to check the battery, the indicator on it showed four green lights, but it lost 1% of its charge in about 2 minutes. What do you all think? Battery? Charger? Something else?

Thanks in advance,

Dave