I have water running in small amounts into my floor board on the passenger side. It traces to that screen under the dash but does it with or without ac on. It's not the heater core because there is no smell and it's pure water.

 

My old dodge did the same thing, it wasnt the heater core either. I believe it had something to do with my Ac, does your ac still work?

 

cowl drain plugged or windshield seal

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or heater box drain