Do you know why switching the solenoids did not reverse the direction that wouldn't work? Before I switched them it would only go down and I assumed that if one of the solenoids was bad it would only go up after I switched them. However it wouldn't go up and it only clicked when I tried pressing down, I agree that it's probably clicking because of corrosion but I would expect it to happen when I try to tilt it up and not down after switching them.

Bad solenoids. Don't buy the quick silver ones, half of them don't work new. I bought six of them at 27 bucks a piece, only 3 worked. Summit racing equipment part # var 93980 for 15 bucks each work great here is a pic
https://goo.gl/photos/69ZhxTTWjnoztngf8

Won't go up can also be wires to the trim limit switch. So you may have switched a good sol with a bad one and put the good on a circuit with another issue. If a sol clicks and doesn't fire the motor, it is bad.

One easy way is to use a wire with alligator clips on it. One end to battery power and and touch to small positive post that supplies the magnetic coil. If it clicks your not making contact across the two larger posts. You can also use the clip on large post to see if motor runs. Then connect the two large posts together briefly with the wire, the motor should light up. The solenoids are pretty simple the two big posts are just contacts, they get arc burned and build a barrier on them. They can be taken apart and cleaned. You have to clip the small coil wires at the solder and pull out the coil(magnet) and you will see the how the contacts work. I just bought new. Like I said the quicksilver or summit racing equipment # var 93980

One easy way is to use a wire with alligator clips on it. One end to battery power and and touch to small positive post that supplies the magnetic coil. If it clicks your not making contact across the two larger posts. You can also use the clip on large post to see if motor runs. Then connect the two large posts together briefly with the wire, the motor should light up.

Same solenoid as the slave solenoid for the starter.

Ken