Solenoids with shorted to chassis negatives are rare. Going from 12+ to solenoid S terminal and no noise no spark means the starter motor interior may have a high resistance condition in brushes, armature or field coil. Not powering the magnetics enough to pull the plunger. Regardless it is time to pull the starter for a bench test.
A bad neutral safety switch blocks ignition switch signal to the starter or to an added relay.
An added relay can go bad as well as wire circuits feeding it.
Only organized diagnostics will pinpoint the problem. Jumping the solenoid is perhals test five of eleven.
Good luck :)