If you have a Digital Multi-Meter, measure for any voltage at any of the cable lines in the house. Do not do it at the Static block on the side of the house, until you go to each line in the house to check for any voltage on the coax lines. Once you find if there is any voltage, then go to the line that is at the static block outside, that goes to the first splitter, and check at that line between the splitter and static block for the CATV company. If you measure voltage, contact the CATV company and an electrician both.
Usually if there is a sign of voltage on the coax, that means you have either grounding issues inside the house, or a loose Neutral. If everything checks out and the CATV states it is not on their end, but the electrician states it is on the Power Company side, then contact the Power Company and request a line check from your residence to their transformer.
If the CATV company unhooks the coax from the static block, and there is voltage on the line, you have a loose Neutral, you will have more than blown HDMI ports, it can cause a large electrical surge through the house, that can knock out anything connected to outlets. What happens, is that your coax now becomes the return path to ground, because there is no Neutral, or a corroded Neutral connection.