You were sent the wrong AC adapter for your machine. All 15" and 17" Aluminum PB G4s came with 65W adapters, and should be used with 65W adapters for best performance and convenience. Furthermore, it sounds as though the 45W adapter you received may be defective, given the fact that the light on its plug is green even when it's charging your battery.
If you have a working iBook adapter, connect that to the Powerbook and see whether the light on its plug is orange when it's charging.
Regardless of how that test turns out, you should demand a properly functioning 65W adapter from the seller.
EDIT/CORRECTION: When I posted the above, I was thinking you had definitely identified your 15" Powerbook as one of the Aluminum models. In rereading your original post afterward, though, I realized that you hadn't. If it's a Titanium PB with a processor speed of 800MHz or slower, a 45W adapter is correct for it. The adapter's plug should light orange when it's charging, though, and if yours doesn't, it's not working right.
Message was edited by: eww