Some questions. There is a small piece of sheet metal that goes between the starter and the mounting surface, was that put back? Who did the rebuild? Store purchase? If applying power directly to the starter motor causes it to spin up then the solenoid that is on the starter is bad. That should have come rebuilt along with the starter. Did you inspect the flywheel gear teeth before putting the starter up? If the teeth are intact, the bendix spring may not be working properly, again, part of a starter rebuild. Sounds like a trip back to the store where you got the rebuilt starter from.
Participate in life....Keep movin'....Go there....JK'n it.........Do it! Jeep #1: Red Rock 08 JK Rubicon 4dr, 6 sp manual, Stock Mud Tires, MyGIG Upgrade, Hard Top, after sale BestTop SunRider Soft Top, Congo Cage Rack, Mopar slush mats Jeep #2 Black 08 JK Rubicon 2dr, 6 sp manual, both tops, some chrome...uggg (my wife's jeep) Jeep #3 White 92 YJ (my son's jeep) A great quote from a good friend: "All hail click clack and master jk'n." Click and clack are my idols!