Sounds like its either the XLR connection or GNX3.
About the only way to check the cable is to use an XLR to 1/4" adapter and plug it into the amp & see if it still works. Either that or take it to somebody who has an XLR input you can test it with.

Basically you just have to narrow it down to the most likely culprit. The mic obviously works. I kinda doubt that it's the GNX3 cause in my experience it's usually the cables or connecters at fault.

The last thing I'd check before thinking it's the cable would be to check the presets and controls on the GNX3 and see if there's a volume control for the mic. It might just be turned down.
Also check to see if there's a line/mic input switch of some kind.
If it's switched to line input, you'll get no signal.