1. Ground seems good, the starter starts up via remote.
2. The batter/charging seems good, back to a remote start showing battery to ground as good.
3. Solenoid is between the starter button and starter motor.
4. Back to a solenoid to a starter button and said corrosion/poor contacts internally say?
5. Say you try a solenoid and see what happens. With the start button, it either lights up the solenoid wire with a test light which means, that's all it does is makes the wire hot so the solenoid creates a magnetic field, pulls the pin to make contact; as if you took a screwdriver to the studs and directly feed current to the starter. Make sense?