A hot connection implies that excessive current was flowing when there should be none. You rig cable and the cable should both be grounded. I doubt that this came from someones satellite system. To bad you didn't measure the voltage from the cable to your rig grounds.
Plug your rig into a GFCI circuit and turn on various equipment to make sure it's not your rig.
Typically the cable goes to the OTA switch or an independent switch to choose between OTA and cable. Then on to splitters to the various TVs.
Does the OTA work? Run a temp coax from a known good cable to the TV to determine that the TV is OK.
Use a wire tracer to trace the coax. Check each segment for opens and shorts. At this point I'd consider just replacing each connector as they and a crimper are inexpensive. Or connect a TV to each segment down the line to see where it stops working.