Legal Question in Civil Litigation in Michigan

It is not possilbe to say whether you and your brother had any sort of an agreement as to who is responsible to maintain the car. You used the car for about 3 months. This is worth something, and if he didn't charge you, then you were unjustly enriched. Unless you can prove that he INTENDED for you to use the car, without having ANY obligation, then you owe him a reasonable amount of money for the use and upkeep of the car. Just because the car has 300,000 miles, it served you well for about 3 months. What would it have cost you to rent a car for 3 months? Offer that amount to your brother. The car may not be worth fixing, but it's his car, his call.

Just considering the practical points of your post, the condition or failure of the drive shaft has nothing to do with a failure to put oil in the engine. You might as well speculate that a windshield crack caused your muffler to fall off.

As far as the legalities go, tell your brother to suck it up. Your portion of the 300,000 miles is minimal or as we say "de minimus". Also tell your parents that he's bothering you and make him stop.