Might be a long shot (not that familiar with Harleys, but know vehicle electrical systems pretty well), but my first instinct given the description would be to check the primary cable to the starter. If there are 3 wires going to the starter, or even two wires if the starter is self-grounding, go for the biggest wire. Generally, one wire goes to the solenoid, and one goes to the coil on the starter. If it has a fusible link in it, check that. Check continuity and/or resistance on that big wire. If the solenoid engages but the motor doesn't turn, the starter cannot be getting full voltage/amperage, especially given that the starter is new.
Hope that helps...man, I hate freakin' electrical gremlins.
Hope that helps...man, I hate freakin' electrical gremlins.