Rarely a starter can have so much drag or a very poor starter cable or connection can suck all the amps out of a battery, there is nothing left over for the coil to fire off the engine.

However when you release the key, all the battery's pent up energy can be diverted to the coil and either succeed or try to anyway fire off the still rotating engine.

Unlikely, however at times when you hear hoofbeats, it really may be a Zebra and not a Horse.

Run a jumper from battery positive to coil positive, bypassing everything in wiring that is the more likely problem. If starts, work backward toward ignition switch thru all wiring and connectors. My money is on this or ballast.