YOu said with the polarity reversal on teh box the A/C did not work.
The thing is. UNLESS you have somethign like a Progressive EMS or a TRC Surge guard which would have told you on it's face (or remote) what the problem is.. The A/C really does not care about polarity. No AC (Alternating current) device cares about polarity.. The issue is important only for YOU...
WHY. Well AC current flows the same no matter how you wire it up. but if it's backwards the danger of shock to YOU goes up. Seriously UP But the device actually can not tell unless (Like the Progressive Industries EMS) it is designed to do so