Most non-grounded devices, especially passive or traditional transformer/rectifier power supplies, aren't affected by reversed polarity. In my eyes, the device sees the polarity reversing 60 times a second. I'm well aware that it's "referenced to ground/neutral".
It is possible that the modem has some circuitry that detects reversed hot/neutral to avoid sending voltage down the coax's shielding. It really should be electrically isolated but nobody really knows without analyzing the circuit design.
I'd take a look at the prong thickness as something too thin may cause a bad or no connection. It's not likely but possible
Ground differentials are what usually cause people to get shocked. I sometimes setup equipment in an industrial building that has circuits coming from from two separate breaker boxes. While plugging in a signal cable from equipment plugged into the other box, I felt a decent shock. I was handling the metal housing of the cable. I suppose it's also possible that something was miswired and one circuit was on a different phase. The building is over 100 years old so many people have worked on the electrical system over the years
It is possible that the modem has some circuitry that detects reversed hot/neutral to avoid sending voltage down the coax's shielding. It really should be electrically isolated but nobody really knows without analyzing the circuit design.
I'd take a look at the prong thickness as something too thin may cause a bad or no connection. It's not likely but possible
Ground differentials are what usually cause people to get shocked. I sometimes setup equipment in an industrial building that has circuits coming from from two separate breaker boxes. While plugging in a signal cable from equipment plugged into the other box, I felt a decent shock. I was handling the metal housing of the cable. I suppose it's also possible that something was miswired and one circuit was on a different phase. The building is over 100 years old so many people have worked on the electrical system over the years