Hello tbone.. and Welcome to this often fun Forum...
If the starter is getting full voltage when attempting to start the engine, there should be no difference between starting with a good battery OR starting with a boost from another battery...Check voltage at the starter While it is attempting to start the engine.
Your starter could be dragging, Is the cable at the starter getting HOT while trying to start? Does it get HOTTER when you jump start? If you have an Inductive Ammeter you can measure the actual current...
If it is dragging you may have a cracked magnet, bad brushes, worn out bushings or a short in the armature... :smile:KennyV