I bought a new Plasma MKII Cannon and equipped it and also configured it through Weapon Configuration so it's on the correct Ports and is the primary fire. But when I try to fire the weapon, it doesn't fire at all, is this a bug with the game or something I have forgotten to do?

This is the Plasma Devastator MkII correct? I would double check and make sure that you have it set for weapons group 1. Large port weapons tend to be placed in weapons group 3 by default.

No, it was the Plasma Cannon MkII <- that's what it says in the game. But now it just randomly started to fire, so it's all working - pretty strange

Try another weapon in that slot, or better yet, try a different ship (even a stock bus) and see if you are still having problems. Perhaps your keyboard/mouse/joystick is starting to have problems? Just a thought.