So the battery has a free replacement warranty for a certain stated amount of time.
Guess what, that means you are entitled to a free battery replacement.
Any charges that were not pre-approved by the retailer (Wally world) they are not compelled to pay (because they would have paid for what the warranty system will pay rather than what you did)
By the way your car ruined the battery, killing a battery completly flat reduces the life of the battery by a massive amount, repeated will not start because it is so dead will ruin it very quick
So guess what: They could probably use the abuse it has suffered to deny any type of warranty, but they won't.
And that is how warranty works
By the way it does not help your case when you yell at the staff or manager.
Cool huh?