I know the pins inside carry the +5v and the other signal but just curious if it's a bad thing to have the outside metal plate of the hdmi connector touch the metal bracket of the pc.

In other words, the HDMI cable is going into the sound card of the pc, but the outside metal part of the HDMI cable connector is very close to the metal frame of the pc almost to the point of touching it Just curious if anyone knows if this is a bad thing.

Reason I ask, is my denon keeps having it's front right channel going out and was wondering if this potential shorting from the hdmi cable connector had something to do with it. The cable appears to carry the signal fine, so not sure it makes a difference if the outside metal part of the connector is touching something.

Mine touches with Xonar connection

I doubt it that there would be a problem. The connector shroud is there to protect the inner pins from both physical damage AND noise. You may have some issues in that domain with poor grounds on piece of equipment versus another and that "condition" finding its way thru via this "connection" as the shroud is connected end to end in the cable.

Reason I ask, is my denon keeps having it's front right channel going out and was wondering if this potential shorting from the hdmi cable connector had something to do with it.

Rest assured it has nothing at all to do with your problem.