PowerBooks, with a couple of minor exceptions, have a clock/PRAM backup battery inside, usually a Li-Ion rechargeable battery that can last nearly ten years or which can punk out after five years or so, depending on the luck of the draw. When the clock comes up set to baseline (midnight GMT January 1, 1970) repeatedly, that is a dead giveaway that the backup battery is kaput. That being said, the main battery should hold things up for quite a while, unless it is tanking as well. (More on that below.) There are relatively easy fixes for the problem that we can point you to.
What is the specific PowerBook model giving you this problem? Screen size, processor speed and machine model. Launch System Profiler in your Utilities folder in the Applications folder. You should see a Hardware Overview like this in Tiger:
Hardware Overview:
Machine Name: PowerBook G4 15"
Machine Model: PowerBook3,5
CPU Type: PowerPC G4 (3.3)
Number Of CPUs: 1
CPU Speed: 1 GHz
L2 Cache (per CPU): 256 KB
L3 Cache (per CPU): 1 MB
Memory: 1 GB
Bus Speed: 133 MHz
Boot ROM Version: 4.5.3f2
Copy and paste that into your reply, Do not include the Serial Number for the machine. Then click the Power line under Hardware in System Profiler and copy the battery and charger information there into your reply. That should give us some information about your main battery as well. It should look something like this:
Battery Information:
Battery Installed: Yes
First low level warning: No
Full Charge Capacity (mAh): 5527
Remaining Capacity (mAh): 5405
Amperage (mA): 0
Voltage (mV): 16553
Cycle Count: 0
AC Charger Information:
AC Charger (Watts): 65
Connected: Yes
Charging: No