I replaced the brake switch a couple months back. My BAS/ESP light was on and the wing would not retract. The new brake light switch cured that problem, but the car would always start and ran fine. I doubt changing the brake light switch will help with your problems.
I would first be certain you have a good ground as Steve Jr recommends, and I would also test the starter to be certain that is not your problem. Isolate it from the car electrical, disconnect both positive and negative battery leads and then supply just the starter with 12v power to be certain it is good.