It is unlikely the HDMI cable was damaged (everything else around it would be in much worse shape if there was enough power to melt the insulation between the wires). Although it could be possible that the HDMI input on the TV, or the output on the receiver, was damaged.
If the TV has multiple HDMI inputs, try using a different one.
Unfortunately, you're going to have to get at all the wires to properly troubleshoot this. You have to pull different components out of the chain, and see where the loss is occurring.
