Trans doesn't go in gear. Now what?! Please Help

Thanks for the input! I appreciate it. Is there a way of testing to make sure the pump gears are ok? Like I said, the new auxiliary trans cooler is warm. Wouldn't that mean the pump is working? Should I try disconnecting one of the hoses? The converter seemed to go in just fine. The flexplate lugs were about 3/16" from the flexplate mounting surface.

The only way to test that the pump gears are ok is to either pull it apart and visually inspect them to test for fluid output. Since checking for fluid output is the easiest I'd pull a cooler line and put it in gear to see if it pumps fluid, even if it feels like the lines are warm.

Not sure I understand this. The converter was ordered for a 727, so I assumed the input shaft fit the converter. Would I know this by how it 'clicks' into place and spins during the install? How would I know if the reaction shaft support fit correctly? Everyhting seemed fine when I slid it into place.

The reaction shaft on all 727's are the same so it's a given it'll connect up but as I mentioned 66 and earlier 727's used a smaller 18 spline input shaft. If that's what you have and they sent you a converter built for a 67 and newer 727 the converter will slip in place just fine but the input shaft won't engage so the car will not move.