Hello & welcome to the site! Does your S&S cooler have a belt-driven compressor, or a sealed compressor?
If the system is cooling I'd suggest that you not disturb it. (if it aint broke-dont fix it), but if your condensors cooling fan isnt working, it's easy enough to replaced on a full size chest cooler. for newbe's I'd say dont start tearing up the cooling system unless it in need of repair.
If the unit isnt cooling however, first, address the wiring issues & then check so see if the compressor will run, sometimes a compressor can be stuck from sitting so long & the original start-run relay may not give the motor enough of a kick to start the compressor running. then you'd like to try a 3-in-1 starter/booster to replace the original start-run relay, the 3-in-1 will give the compressor an extra little kick in the pants to help it start up.
if it still wont start & only hums & then the overload breaker clicks out (in the 3-in-1) now you have a mecanical issue internally ( inside the compressor)
if the compressor is running & not cooling , unless you are handy with brazing, then you wil have to install a clamp on type of service valve onto the low side line (suction line) , thisis the large diameter line that comes out of the tank above, pick a spot that's easy to access & has a nice round section of tubing, CLEAN the copper line with some fine steel wool to remove any oxidation & dirt. (make it shine like new copper) were you are going to place the valve.
also note that the best way to check a system for leaks isnt with a vacuum pump & gauge, but with working pressure in the system & a refrigerant leak detector ( bubble type detection liquids work on larger leaks)
Beware of units that are for sale that state " compressor doesnt run, but just needs a "shot" of freon" this is another way of saying they are trying to sell a machine with a blown compressor. if it runs & cools only then it's a working
machine, if they cant prove that it runs & cools. then adjust your purchase price accordingly. (figure in $300/less for a new compressor replacement)
As mentioned in a prior discussion area, also beware of "cant test becuse the plug has been removed" & "line cord has been cut off" "worked a few years ago". "work last time I used it years ago" etc. they are just dodging the fact that the bloody machine has big metal turd were the compressor used to be. and they know it.
as for how much of a charge of freon you may need , other members with simular S&S chests may be able to tell you what the info tags say for their machines.