When he says it won't start does he hear the starter solenoid click? That makes a big difference. If there is no clicking from the solenoid, I personally, would go after that damn ignition switch module. GM has had tons of problems with ignition switche modules in all their vehicles. Could also be a bad ground, and just moving wires around might allow it to make better contact. Also have them double check those stupid battery terminal connections. They have to be very tight and the ones on the H3, we all know are not the best ever designed.
If the solenoid clicks but the starter does not turn over the engine, I would look at the battery cables, the major grounds off the battery negative cable. I would then hit the starter, not to hard with a hammer or large screwdriver, butt of the gun, etc., and see if it then starts. (That would indicate an internal problem inside the starter.)
Other than that, intemittent problems, if no codes are set, are sometime impossible to correctly diagnose. Hopefully, new parts will cure it for no other reason than pure luck.
GONE FROM THE HUMMER WORLD!