My laptop will not charge when I am using my HDMI port, what's wrong?

The question title relates to my most immediate problem as I am trying to do some design work and a doing it without a larger than 13” monitor is a real pain.

A few things to note about the machine. Issues that may or may not be connected.

The left USB port does not work and no sound is available.

The keyboard and trackpad don’t work - this has been professionally diagnosed as a faulty ribbon which I will be replacing as soon as the part arrives.

Any light shed on the main question would be great, additionally some troubleshooting on the inactivity of the sound and USB would also be great - I have a hunch that it’s a hardware thing.