Re: 2003 FLHTCUI is possessed with an electric gremlin
You have been inside the fairing and with the problems you are having , I would look for a loose or bad ground. Also check to see if the ground strap that may be at the bottom of the risers is intact too. It furnishes the ground to everything on the front end. Also check the individual grounds too inside the fairing.
Try this, get a piece of 14 gauge wire and connect one end to the negative of the battery and touch the other end to the bars and see if everything works then. It's a quick way of testing the bike ground to the bars to see if that's the problem.