ok so you verified it works with it removed
the problem with checking it while hooked up is that you will probably get a 0 volt reading, disconnect it and check the harness side (not the solenoid) and see if it is getting battery volts. If not then you will have to back trace the circuit through the harness till you find the issue. Check all the harness connectors for corrosion etc, if you run across any relays or circuit breakers check them as well.
Everything usually sprouts out from the fuse panel so since you did not find any issues there it is probably between the fuse panel and the solenoid somewhere.

But the fact that it seemingly is running without the solenoid working properly tells me there is still something wrong with that solenoid, the plunger or something.