You will see a slight amount of voltage drop at the solenoid depending on the solenoid coil draw and size of wire that you are feeding it with. 4 volts is way to low.
I think you will find that when you jump the starter its going to crank over fine.
At this point, I would say you have bad wiring, ignition switch or neutral safety (if you have an automatic).
Don't worry about the voltage coming from the old R line. Not sure what mods you have made but you are just getting backfeed from the ignition circuit.