Why don't you try starting from the beginning. That's what I always did going on a service call
1. Is the thermostat set to the lowest temp?
2. Are both batteries good (Reading at least 12 volts) Verify all cells are good.
3. Restore the battery wiring as it was at first.
4. Check voltages when charging, not charging and under load (run something 12vdc)
5. If all is good connect the battery to the existing battery by placing the wire ring on the battery post neg to neg, pos to pos without removing any of the existing wiring.
6. Now try it and see what it does.