Man, that game just ticks all the boxes. It must be it!
I did check out all the other suggestions that were made here, but most of them were released for the Amiga and I know all games for that machine, and it never rang a bell. Trauma sounds completely different to me, too. Was surprised by Starglider, but thats not it either
So yes, it must have been Goldrunner and perhaps I somehow started mixing it up with other games that were on display, I believe Ikari Warriors and Space Harrier, both games with lots of "greens", but no speech.
Thanks all for your help!