Logic Board replacement for water damage. Worth it?

The issue i’m experiencing is that the battery is not being recognized. I will start by saying there was water damage within the firewire port. This is what I believe caused the issue but I’m not 100% sure.

The computer is fully functional, however it only works when hooked up to the power source. I tried replacing the battery with a known good one as well as a known good charger and the same issue persists.

The next step for me is to replace the logic board. I’d ideally like to make this as cheap as possible and do it myself.

The cheapest logic boards I found run about $200 for “like new” and tested from retailers like Amazon, etc.

Question 1: Will this most likely resolve the issue I’m having?

Question 2: Since it is an older model, is it worth it?