It's a speaker cabinet so it shouldn't take much more than a phillips screwdriver and perhaps an instrument of prying to dismantle.
First things first, make sure it's not just a bad speaker cable. Then, check external sources of buzz. It could have been something in the room, even if it seemed like it was coming from the cabinet. If could also be one of the handles, the grille, caster wheels, or one of the components mounted on the jack plate. Check to make sure the hardware's fasteners are snug and try playing through the cabinet with the grille and casters removed to rule those out.
If that all checks out, gently press on each driver to exercise the cone back and forth a little. If you hear a scratchy rubbing noise, you may have a burnt voice coil. If not, check to make sure the crimp connectors on each driver are seated tightly. My Ampeg 4x10 had a slight buzz on one speaker from a slightly loosened crimp connector. I usually disconnect each one (one at a time) and give the prongs of the crimp connector attached to the wire a gentle pinch with a pair of pliers. This will give it a tighter fit on the speaker terminal tab. I'm not sure on your GK, but you could also have thumbscrew terminals on your speakers with bare wire inserted in them instead of crimp connectors. In that case, ensure those have not worked loose.
Since your cab has a horn crossover, it's worth checking to make sure the mounting screws for the PC board standoffs holding it on the jack plate have not come loose. For that matter, it may also be worth checking that the horn's crimp connectors are tight and that the plastic horn is firmly attached to the high frequency driver (sometimes they are two separate pieces screwed together) and that the whole assembly is firmly attached to the cabinet.
If none of the above fixes the issue, it could be a bad input jack or a solder joint on the crossover board. I believe those cabs have one Speakon and one 1/4"; try the other jack if you have an appropriate cable. As for a solder joint, you may be able to spot it, or you may just need to reflow the critical solder joints like around the jacks or the wires that go to the drivers.
If you still have a rattle, it could be the cabinet itself if some of the bracing has come loose. Newer cabs like the GK Neos most likely are assembled with modern catalyzed glues that should keep a strong bond, but it's worth checking.