Axel didn't mention in the original post / question that he had replaced the AC adapter.
Question: My PB 15" 1.67 GHz from December 2005 does not run on just the AC adapter.
It quit working / turning on, and the battery has the first light that is blinking rapidly. I replaced the faulty battery (that Apple sent on the second day I had the PB because the first battery that came with the PB would not charge) with the battery that came from the previous PB (15" from 2004).
That replacement battery took a few hours to charge. After replacing the battery, the PB functioned normally, and the battery showed a full charge.