727 no 3rd wont shift

It could be a throttle pressure linkage (kickdown as everyone calls it) issue but generally that won't cause it to not shift at all. To make it shift earlier you want to shorten one of the rods so it's not pushing so much under hard throttle. If the linkage adjustment doesn't help it is a governor/valve body issue. What year trans is it? I ask because a buddy of mine bought a 90 Ram with a 727 that wasn't working right and I found that who ever rebuilt it clocked the rear output shaft support wrong and it was doing just what yours is doing. Earlier 727's only had 4 bolts and they were staggered so it only went on one way. The later ones used a 6 bolt support and the bolts are evenly spaced so if you don't watch closely you can install it wrong. If you do clock it wrong it blocks off the governor ports and makes it not shift right.

One last question. Does it start out in 1st gear when the shifter is in drive or do you have to pull it down into low for it to start in 1st?