Your alternator is dead. If the contacts/copper get encrusted and/or too wet to the point where they get surface corrosion, that's the end of your alternator (unless you rebuild/clean it).
You can clean your engine compartment CAREFULLY with a hose. The trick is to do it with the engine WARM, not hot. I typically hose out the chunks, avoiding the more tender electrical stuff. Then, I'll literally wash the engine compartment quickly with soap/sponge and lightly hose it out. Then I immeadiately run the engine and let it idle for 10 minuted to dry itself off.
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00 TJ BDS lift, 33" BFG MTs, locked