The voltage measured on the coax doesn't tell the whole story, especially if it's measured with a high-impedance digital multimeter. The two cable boxes will have isolated power supplies inside, meaning their low voltage circuitry is isolated from the high voltage mains. But there can be capacitive effects that would cause a voltage to appear between the mains and the low voltage circuits (ie the coax connector) even though there's no path for a meaningful amount of current to flow.
To check whether that voltage really means anything you'd need some kind of load. I'd grab a resistor in the range of a few hundred to a couple kilo ohms from my parts box, put it between the cable shield and ground, and measure the voltage again. It should drop to near zero.
I'm trying to think of an alternative that a "normal" person who lacks an electronics parts box might try instead.. If the meter supports current measurement, one could measure how much current will flow between the cable shield and ground. Use an ordinary incandescent or halogen light bulb (not LED or compact fluorescent) in series to limit the current in case there actually is a fault in the cable boxes. A regular household bulb, a large C7 or C9 bulb from old-style Christmas lights or a night light, etc will do. Using your third and fourth hands (or an assistant) put the meter into its highest-range AC current mode, hold the coax cable shield to the shell of the bulb, and touch the meter leads to the button terminal of the bulb and the electrical ground. Repeat with the meter in DC current mode. (Don't forget that meters usually require the red lead be moved to a different socket for measuring current, and definitely remember to move the red lead back to the voltage socket immediately when finished!)
If the voltage didn't drop to near zero in the load resistor test, or if the meter measures more than just a few mA in the current test, that could be a problem and replacement of the cable boxes could be advisable. If these tests check out ok it would seem that the energy that melted and burned the demarc probably didn't come from those two cable boxes.