If the switch is going into lamp test, gauges are arming, doubtful it's the rod. Just check make sure its fully seated in the switch. From there if good, check electric as suggested.
Easiest is to check the small terminal at the starter. If it energizes (12VDC) at "start" and still no crank, check the large terminal on starter. It should be hot all times. If so, then issue is solenoid in starter. Pull the starter and bench test.
If no volts at small terminal when in "start", then it's in the circuit from switch to solenoid. You will have to back trace circuit.
Also check simple stuff first like fuses, fused links, circuit breaker (30 amp metal can style). Check and make sure all connectors are pushed all the way in, no burnt or frayed wires, etc...
Then always a possibility even if new..., the switch may be bad.