My daughter's 2001 CR-V stalled while sitting at idle with transmission in PARK. I checked for spark at all 4 plugs and got none. I checked for spark at the ignition coil and was successful. I went to replace distributor cap and rotor, but could not get the rotor off. I assumed it was rusted. I eventually broke the rotor and removed it. When I tried to place the new one (which is identical), it would not go on the shaft. I turned it 180 degrees and it slipped easily on. I had to bump the engine to rotate the rotor so that I could get the set screw in.

My question is, how is it possible that the engine ran with the rotor obviously installed incorrectly before? Should I force the rotor on the same way it came off? It still will not start with the rotor on correctly. (Flat side of rotor aligned with flat side of shaft).

 

You can put the rotor on the rotor shaft incorrectly and still have the car run if if the rotor shaft has been installed incorrectly or the plug wires have been swapped around.

I would find cylinder 1 TDC compression stroke and then align the rotor with that pole on the cap.