Crutchfield has an internal photo. The ribbon cables will be data cables. I see 3 other white plugs, one in the back, one in the front and one hidden on the right, which may carry power. There is a vertically oriented circuit board in front of the HDMI board with a long row of pins. It appears from that angle that the two boards are joined along that row of pins. That board could possibly be supplying power. Really need a service manual to know for certain.
I think it's unlikely that you can get the HDMI board powered off and still get the unit to function. A skilled repair technician with a hot air solder tool could unsolder the offending chip that is getting hot. That's the only safe way to continue to use the unit. Have to agree with TLS, sadly. This one is destined for recycling. Even if that chip is available for replacement, there could be other issues with the HDMI board that show up afterwards.