Assuming the battery is not working, I know of no other way to access the data without ripping open the PowerBook. Third-party adaptors are still available and the price is much less than Apple used to charge:
The other option is, as I hinted above, to open up the PowerBook and extract the hard drive. Once out of the powerbook you use a device like this:
It allows you to attach the bare drive from the PB to a USB port on teh MacBook Pro. The drive will appear on the MBPs desktop just as if it were and external drive in an enclosure.
Are you sure that the problem really is with the external power adapter (and its cable/plug)? Generally speaking, many laptops (Mac or PC) have DC-in jacks (inside the computer) with soldered pins that work loose. The typical sympton is that the supplied power is depending upon the position of the plug. Often, someone with basic soldering skills can carry out a repair by simply resoldering the pins in question.
Otherwise, you would have to use a generic hard drive adapter similar to the one Allan suggested (the second link above).
For computer disassembly instructions, you may want to have a look at (for example) the ifixit.com guides.
>The typical sympton is that the supplied power ...
The typical symptom is that the supplied power ...
Some laptop computers have a separate DC-in board that can be replaced, without resoldering any pins.
As you can see from the ifixit.com guides in question, the level of difficulty regarding access to the DC-in section or the hard drive depends on the exact PowerBook G4 variant/model.