I'm going to try moving you over to the GL subforum. I don't think you're wrong asking for hardware advice but it's more likely someone with a similar laptop will read it.
As for the issue, I think you were on the right track trying to choose PCM. Often no audio is a sign of an incompatible format. The only other way to test would be running HDMI to another device like a home theater receiver that should support all formats. I know that probably isn't an option but perhaps another TV at a friend's house?
Also, if you are fed up and just don't want to deal with it then another solution would be to buy an HDMI audio injector and just always use the internal sound with the 3.5mm jack. I know that's clunky but it would solve the problem.
A bus station is where a bus stops. A train station is where a train stops. On my desk, I have a work station…