Any wire has the capability of carrying current, including HDMI cable.
Under normal operation all AC power should be on the AC line and not the Video connections.
When a device fails, then many times the devices MOV puts a direct short across the AC line input, and blows the device fuse.
When you add a set-top Box with a cable or Ethernet connection then power will complete a ground path thru any possible path that it can find, Video, RF, Phone lines. Ground Loops are very common with things connected from multiple locations.
You may want to power down your HDMI switcher completely and see if it will reset, maybe it got stupid.
All devices connected together should be on the same AC circuit if possible, and a Three-Way surge protector should be used on all devices.
If the devices power on, then the built in MOV and fuse is still good, If the HDMI port is damaged, then repairing it would depend on the unit itself.
Have a great day.