Well, Steve, it sounds to me like the brushes or the armature in the motor got toasted when the motor stalled under the high load. It is also possible that the reversing solenoid contacts have failed from high current and heat. The solenoid is the device producing the clicking noise.
If you have one of the Simpson Lawrence windlasses like the Anchorman 1000, the original motor was made by a French company called Leroy Somer. The motor is known for its problematic brushes and poor reliability. Couple that with a gross overload when pulling an anchor, and you have a likely opportunity for a failure.
If you have a different windlass, the problem is still most likely the brushes or the armature, but you may not have the pre-disposition of the motor for failure.
Either way, you are looking at removing the motor for either replacement or service or replacing the solenoid.
Here is how to troubleshoot-
Remove the fiberglass panel inside the vee berth so you can access the windlass and the solenoid (see picture below). The reversing solenoid is a large relay that has four large connecting studs and three small connections. The small connections are wired to the foot switches and those circuits are obviously working because you hear the clicking of the solenoid.
The battery wires are both connected to two of the heavy studs and the motor wires are connected to the other two studs. The job of the reversing solenoid is to connect the battery to the motor with one polarity to raise the anchor and the opposite polarity to drop the anchor.
If you place a voltmeter across the two studs that are connected to the motor, and have someone operate the foot switches, you should measure about 12V at the motor studs. Depressing one foot switch will cause one polarity of voltage and depressing the other switch will cause the polarity to change. If you observe this action, then the solenoid is most likely OK. If you do not measure any voltage at the motor studs when the solenoid clicks, then the solenoid is toast.
If the solenoid is good and you have voltage at the motor studs, then the motor needs to be removed for service or replacement.
If you have a Leroy Somer motor I would recommend replacement with a different manufacturer. If you have a motor manufactured by someone else, I would take the motor to an electric motor repair shop for evaluation and repair.
I have a source I can recommend for a replacement motor for the Leroy Somer if that is what you have. The vendor is in the UK and the motor with DHL air shipment will cost about $450. Email me from the Hunter owners directory if you need the contact info for this vendor.
BTW, after rebuilding my Leroy Somer motor twice and still having failures, I replaced my motor several years ago and now have flawless operation.