[Jebus]

If it has done very few miles, for several years it has likely either say in endless amounts of traffic, never been revved and not had engine oil changed so is just a bit gummed up.

If the test of unplugging the solenoid when idling works, it is the pulley that is worn so will need replaced at some point.

However, a few good oil changes, treating it like you should and using a good oil, will do wonders in keeping it running sweet and will keep the oil system clean, it has likely gone years without an oil change, and anything that relays on the oil system to work doesn't respond well to lack of oil changes.