Is it normal for coax cable to carry this much voltage?
Likely source of the problem is a bad cable box.  Transient voltages or surges from indirect lightning can damage electronics. 

You could test the coax shield to neutral or metal pipe that is properly bonded and see what the voltage reads. Disconnect everything from the box as to isolate the box.

I troubleshot one the other day that had 50v on an isolated shield.

Further advice: make sure your home is properly grounded to earth w/ ground rods and/or water pipe per NEC Code.