At the risk of appearing a simpleton, I ask if you cleaned your battery terminals and connectors.
on the terminals can cause intermittent flow, varying flow with varying loads, and varying voltage. As components are made to work in a specific voltage range, this can throw "how it should work" out the porthole.
When you say " I disconnected the solenoid and switch, and connected "it" directly" what was the "it"?
Jumping a battery (in the bow) direct to the winch
with nothing else in the circuit will tell you if the winch
works, Yes or no. You have lots of good advice on what to do with a bad winch.
Add just the solenoid and touch a jumper to the switch terminal on the solenoid from the battery. That will tell you solenoid good or not.
If the solenoid and winch are good, add the switch. If it fails, the switch is bad. If that works, the problem is in your transmission
wires, between the battery terminals and the power lines that attach to the solenoid or the switch. Power lines shorted to ground, bad connection, bad breaker/fuse, could be the problem. load and no load behavior or voltage will vary, as does energy available.
Basically, clean ALL terminals, then start with only a battery at the bow and winch, adding one component at a time.
If the primary problem occurred for some time, it could have caused a secondary problem, which confuses troubleshooting a lot. Both problems will have to be resolved.But deal with one piece at a time, and eventually you will find the bad piece(es), and soon have a happy anchor
Others have said most of this, many said it better, but here it is all in one piece. Good luck!