Firstly you only had their word that it was cold when you bought it. A fridge with a compressor should be kept upright when it is moved and if it isn't it should be allowed to settle for a few hours before switching on. Once switched on it can take several minutes for refrigeration to begin and that would only be known by somebody holding a hand against the evaporator. It could take significantly longer for the interior to cool significantly considering the low wattage of the motor.

I am wondering how long they tested it before declaring it was ok and saleable...

Getting the right polarity when connecting equipment to a direct current is paramount and rarely is there a second chance if you get it wrong - trial and error is not an option, especially if the unit contains electronics. It is possible you got it wrong.

I suggest you take a look through a magnifier at the circuit board tracks. If you find one cracked or burned you might be able to make a repair and be very lucky, otherwise you probably should take the unit to a specialist for repair or perhaps return it to the junkyard as faulty...