A lot of things, probably most, will work with reverse polarity. It's just not a safe thing. So it sounds like you lost
power along with the reverse polarity.
As noted above, check the shore power cord (both ends) and the dock
pylon outlet for signs of corrosion
or black from heat. Replace your cord if you see any. At least replace the end(s) and cut back to perfect wire. Better to just replace since the ends aren't cheap
either and don't seal well.
As noted, check ALL your wiring
from the shorepower inlet (including the wires connected to the inlet) to your panel. Check for loose connections, burnt parts
, at the master breaker close to your inlet (per standards although you may not have this) and the main breaker at the panel. Also check all the wiring
on the panel itself while you are at it. Make sure to turn off all power (unplug the shore power and disconnect the inverter
if you have one).
The PO of my last boat had had an actual fire behind the main AC panel. This didn't show up on the survey
since it "not responsible for inspecting any parts
requiring tools to access". This was not conducive to good electrics.
I have found many surprises working on other boats too from questionable wiring practices by prior techs and/or owners. Good idea to check all wiring over time as soon as you can get to it.