May just be a drain on it somewhere, 5 mins drive wont have added the charge to cover the jump start. Get a volt meter on the battery so you can see the before you start voltage and see overnight etc.
If you started the day literally with enough...
I would be guessing but I would be VERY surprised if anyone could stand by a warranty on a vehicle which is written off. There are so many unknowns and risk which there wouldn't be any appetite for.