Ignition may still work depending where the shaft broke. Usually the hex end in the pump shears - and the engine will run fine because the cam is driving the gear just like normal.
Yes, that is true. But I was trying to give him a quick check. If the rotor does not turn, then you know it is in the drive gear for sure. It depends on how the shaft broke as you said.
I had the two gears "crash" on the camshaft and distributor shaft, and the rotor would not turn. It's an easy check. If the rotor does not turn, then the oil pump should be ok, the problem should be in the shaft somewhere. If it still turns and no oil pressure, then you may want to tear it down and inspect the oil pump and shaft for problems.
I was just trying to start out simple and work towards the "harder" more labor intensive fixes.