Based on what you said about the battery, I'm assuming you just shorted out something in the electrical system. The battery might have just reacted to a short somewhere else. It must have been salt water because fresh water isn't very conductive (distilled water isn't conductive at all). An electrical system problem would definitely cause the engine to shut off though, so the problem may just be limited to that in the context of the battery failure.

Check the engine out just to be safe, because that may be the problem instead.

Before you install a new battery, check resistance between the positive and negative cables (before the battery is connected) just in case there is an electrical short somewhere. Happily, you can almost completely check out the electrical system without trying to start the engine, so you can get the electrical side of things fixed independently of checking the engine for possible hydrolocking.