There are several connections in the starter power line including, I believe, two solonoids. If you can put a meter on the battery and see what the voltage is initially - s/b greater than 12.5 volts - and what it drops to when you try to start. If the voltage doesn't drop much, you either have a dirty connection of some contact is not closing. You may need to trace the voltage line from the battery thru the solonoids to the starter. If the starter has 12+ volts going to it, then you may have a bad starter.
The outdrive raise/lower is a little funky on these,, using an electric moter with a one-shot impact type system. Usually the problem in raising not lowering. You might have dry lubricant on the pins the outdrive roataes on. I had that on mine and after I took them apart and greased them really good, things worked much better.
The fact that it doesn't lower lends credence to the bad connection or possibly weak battery. These system like a really hot battery. I try to keep mine as close to 13volts as I can. Hope this helps, Ken