Okay, then let's deal with your original thought of whether the intermediate shaft is too short since it sounds like you're not turning the pump with the distributor in there.

First things first, don't assume anything. Look in the end of the drive gear and make sure there's a drive tang in there to engage the shaft and that it's secure. Measure the length of the distributor from it's mounting flange (where the clamp holds it in place)to the bottom of the drive gear (the tang should be less than 1/8 " recessed). Take a straight edge across the distributor hole and measure down to the top of the pump shaft. The distributor should be 1/4" longer to get good egagement. If the length is good enough then make sure the distributor is seating fully. If it's not long enough, then you need a longer pump itermediate shaft.