...they tried other power adapter cables and the same thing happened.
That sounds like the problem is internal to the computer. The "barrel" type power connector you can see from the outside of the computer is soldered to a power board. With repeated stress on the connector over time, the little metal "legs" that support the conenctor on the board and also establish the electrical connection can work loose.
It's a fairly common failure in PowerBooks and likely a major reason Apple moved to the the "Mag-Safe" power conenctor on MacBooks and MacBook Pros when they replaced the older notebook series, the PowerBook and the iBook
The first thing to check is if the light comes back on if you GENTLY push the adaptor plug in different direction. If the light comes on when you push the connector up, that's a pretty reliable diagnostic for a loose connector.
People have successfully resoldered the connector to the board but the takeapart procedure for a PowerBook is not trivial and you need better-then average skill in soldering small, heat-sensitive components. Apple will no longer work comptuers older than about five years but you can probably find a third-party Apple Authorized Service Provider that still works on older Macs.
If you give us a general idea of where you are located, prehaps people here can refer you to a trusted service provider.
If you want to look at the step required to "DIY" and decide if this is a taks you can handle at home, here is a link to iluustrated service guides select teh one that most closely matches you PowerBook variant; the instructions are often different for PBs with different screen sizes.
I received your advice to find a local technician to do the repair and not try to do it myself, which I don't think I'm capable of. Thanks for your opinion and feed back. I plan to look for someone in Madison who is authorized by Apple to do repairs. Thanks,