GB. Do the easy things first. I would take the battery to my FLAPS that has a battery analyzer/charger (not just a resistive load tester).
The test takes about 45 minutes and it is free. A charged 6V battery at idle will read around 7.5V.
If the system is not charging it is easy to tell by watching the ammeter.

"Adding CFM to a truck will only help at engine speeds you don't want to use."
"I found there was nothing to gain beyond 400 CFM."