John,
I might not understand your post completely. While jumper cables can be a fast method of wiring, many times they are either undersized, or have very poor connection at the clamps.
Having said that, I not sure on your button comment, unless this is a solenoid equipped rig, which would seem strange for a 216.
A traditional stomp style starter would need to have a good connection with battery positive at the large lug on the little switch on top. There is some linkage that needs to be depressed to engage the flywheel ring gear to the starter PLUS close the switch to provide battery power to spin the starter.
If somehow you have a solenoid starter, the battery connection is the same, and one of the small wire terminals must be powered to engage the solenoid. You can use a screwdriver jumped between the large BATT lug and this small, protruding terminal. That should spin the starter.
My guess is that the jumper cables aren't making adequate connection and the whole thing isn't working. Wiggle the alligator clamps and make sure they are seeing good clean contact and make you ground right to the engine/starter.
Your volunteer battery must have clean shiny cables and have a real good charge too.
Stuart