2002 Jaguar S-Type Electrical Gremlins

We just got home from doing some running around and noticed that the automatic headlights didn't turn off after a while. When I went to check on it, I noticed that the dash lights were coming on off and on and the steering wheel was sliding in and out randomly. I tried putting the key in and the radio came on like it should, but it will not turn over. At all. I tried several times. We went to disconnect the battery and noticed standing water in the spare tire well. We've had a lot of rain lately, so apparently I have a leak somewhere back there. I'm guessing that a relay or fuse or something may have gotten wet? Since we were just driving around, I'm thinking that the water could have splashed on something that's not supposed to get wet? Its acting like I'm putting the key in and out. So could it be something with the ignition? We currently have the battery disconnected hoping things will dry out. Its a really strange gremlin. Seems to have a mind of its own.

Unrelated issue. After a while of running the heat, I smell burning rubber. Any ideas?

Thanks for any help you can give!