PMU and Logic board issues

I have a 5 year old ibook G4. Here are the stats:

Model Name: iBook G4
Model Identifier: PowerBook6,7
Processor Name: PowerPC G4 (1.1)
Processor Speed: 1.33 GHz
Number Of CPUs: 1
L2 Cache (per CPU): 512 KB
Memory: 768 MB
Bus Speed: 133 MHz
Boot ROM Version: 4.9.3f0

My computer has recently developed a problem where my computer randomly shuts off and won't turn back on. In addition to that, the battery won't last more than 10 minutes (this could just be age though). After going through Apple's trouble-shooting site I found out how to reset the PMU. This does work as far as getting the computer to turn back on, but it's a temporary situation. My computer and I have gone through this process at least 4 times. It seems weird that I would have to reset the PMU every couple of weeks (or less) but currently that's my only solution to keep this computer running. Other than replacing the logic board I can't find any other permanent solution. So I was hoping for suggestions.