So what does this mean? It starts in RUN position now with the key, what does it matter that I started the car in the RUN position by jumping it at the relay?

It means that everything is fine with the wiring until your key goes to the start position.

So, you got new ignition switch so we'll assume its working ok but somewhere from the ignition switch on out through the wiring harness there is an open circuit thats not powering up the coil , or the ecm and it could be the bulkhead connector.
if its running good and starting fine in run position, it should be just a matter of elimination to find your problem.
wish i was closer , prolly fine the trouble pretty quick .