Hi MB and welcome to the forum.
I experienced the stuck in park issue and fixed it fairly simply. Can you tell us for instance when you say, "Does not start" are you stating that the motor cranks over but does not fire or the starter does not engage or turn the motor? Specificity will help here. The advice of the cam and or crank position sensor was good if the motor is actually spinning but not firing. You stated that you performed a "resolder" to the RCM and that didn't help. There may be other issues with the RCM that TighEd here on the forum is quite accomplished in repairing and or refurbishing.
~ When I began my search to fix my "stuck in park" issue, I used the forum search and typed ..stuck in park..Several threads came up. You..tube dot com search can be used the same way but the type of car needs to be added to their search. Does your dash indicate a "P" or a black square block? Have you tried to replace the brake switch that runs about 20.00 bucks? Has anyone spilled liquid down the shifter? Look for coffee residue in the carpet. There is at least one video on how to disassemble the console and remove the trim pieces without breaking them in order to gain access from above to change out the shift module. Remove the shift **** first by pulling BTW after releasing the threaded trim ring. The shift module changeout can be done from inside of the car,...final trim covers up bailun wire in case you break a tab...hint hint.
~ Your battery drain issue is going to be fun, and there are several detailed threads here on how to go about identifying the troublesome draining circuit...Good luck on all of it, and I hope this helps you.