You have a tough issue there for sure and there's certainly enough expertise here to get you through it.
Since you're in the middle of a potential fix, I just want to drop these 3 comments until we hear how your new wire run works out.
1. I am with Dave, due to personal experience, that you really should replace that Dimmer switch. They get faulty, cause grave issues, and they are cheap and easy to replace. Do it.
2. Bear in mind that you very well could have more than one issue. Don't let yourself get stuck on a single solution that solves everything.
3. Personally, I really really think you should find out where that mysterious 2nd small wire is going to from your battery post. It might be as simple as a home-run for a radio, or old switch someone installed, or hell, the key itself. People do weird things. If you can crimp or solder a wire (any monkey can!) than you might even consider just cutting it or removing it at the battery and you'll soon figure out what it was for if it serves any importance.
Cheers! Good Luck! Keep us up-to-date!