When you are doing remote starter trigger, it doesn't matter if ignition is on or not. All we are trying to do is test the starter to see if it works.
So one small terminal is to throw the starter gear forward to engage... and one is to turn on the starter and spin the starter. The big wire to the starter is always hot. You can check with your multimeter.
You must remember... BMW immobilizer does NOT cut off the starter. You can always turn the engine over but won't start the car.
If you can't get your starter to make a noise, your starter is dead. Take it out and take it to any auto parts store and let them test it for free... it is most likely dead.