Well you do have a couple of problems here:
First you'll need to replace the PRAM battery if your model has it. Here's the guide to get to it: [guide|249|PRAM Battery & USB Board Replacement]. Some of this series had a clock chip which had it's own battery internally on the logic board.
I do think you have a logic board issue with the charging circuit. The DC-In board does not have any of the charging logic on it. This could be a big job to diagnose and repair.
This system is quite old. I think your money & time would be better spent on a newer system. Don't get me wrong here in its day is was one !@#$ of a system! I had the titanium version for quite a few years.