If your converter is from 1989 it should be replaced. Get a modern converter with three stage charging. I suspect that most of your problems are from an under charged battery.
Having said that though, I don't understand how it runs the furnace OK but not the water pump. Furnace fans are real power hogs.
Try this: Put your multimeter (on DC range) on the battery terminals and note the voltage. (It should be 12.6 or a bit higher if nothing is on) Then while keeping the test leads on the battery terminals have someone turn on the water pump. Note the voltage--it will likely have dropped some but not lots. Then do the same with the furnace.
Report the numbers back here.