[LMP]

If you want to test another battery, borrow one somewhere ...I understood you had already done that. There is no magic with batteries. If the starter cranks the engine at a normal starting rate, you have ample electrical power. IF the battery is low, recharge it first.
IF you end up with a dead battery in the morning, you'd be better off using an ammeter between battery positive and connector to test if there is any stray current when all should be off. THE computer takes a very small current, like 20 milliamps. Then when you have the engine running (remove the ammeter to start), measure voltage : should be near 14 volts.