The reason I'm going with no is that HDMI "chips" are coming with non-updateable code so if there are bugs like you describe no update short of board replacement can fix it. You can research further about this and find others that experience problems with the HDMI handshake system.

Yes it could be a cable issue but nothing in your post tells me it's a bad cable. That is, usually the system works until the cable goes bad. But your system has failed from day one so it's a HDMI chip issue.