I've solved the issue now. PC Engine GT with an apparent "faulty" screen, is now working like a charm (and with loud sound and all!).
Firstly I tested the screen in another fully working GT, the screen worked great - tells me the issue is something other than the screen, i.e. component(s) on the GT's main PCB.
I checked the voltages going to the screen with my multimeter, and compared those to the voltages going to the screen with the GT that was fully working - interesting, I noticed one MAJOR variation in voltage - perhaps the lower voltage was not enough to drive screen output?
I tried to follow the trace, but it proved quite difficult and I lost it.
So then I started looking at the capacitors, thinking a lower voltage was probably a dodgy capacitor. I noticed that on all of the capacitors, where the silver legs are, they were not silver/metal coloured but in fact yellow/brown/dull. I removed one capacitor to look underneath. A brown mess of dried electrolyte!
Every surface mount capacitor on the PCE GT PCB had leaked!
So I went and ordered replacements, getting surface mount where possible, and a couple of strange values/max voltages were replaced with microminiature radial electrolytics.
After reassembling everything the unit now has perfect, loud sound, and a great display (bar one dead pixel!)
So I think the general rule now is, that if you have either of the sound/screen problems, replace all surface mount capacitors (except for the three, large, yellow nichion 16v 100uF capacitors, as I removed one of those and it was nice and wet inside!) all of the smaller surface mounts were BAD!
Even my GT that is working perfectly, has this yellow/brown/dull look to the leads, which suggests the capacitors in that unit have all leaked too!
So glad I managed to solve the problem