ignition won't start; wipers won't stop!

I think you need to find a Chrysler specialist or an auto electric shop. You may need to disconnect the battery to get the wipers to turn off, better than letting them run until they run down the battery and maybe burn out the wiper motor. No It's not a bad battery causing your wiper problem, I don't know what's causing the car to fail to crank and start. Here's a directory link for you: https://repairpal.com/dodge-repair-in-south-orange-new-jersey

I have been having the same problem. Check your (PDC)power distribution center under the hood. Make sure all you connections are good. You can pull the wiper relay if that happens again, to stop the wipers. I have put in a new starter and battery cables and a new PDC. It stopped for a week and now starting all over again. Tell me too if you figure it out.