[drolston]

Sounds like the starter is drawing down the voltage at the battery enough to prevent a spark. The instant you get off the starter button, the voltage pops back up but the engine will continue turning on inertia long enough for it to kick off.

To confirm this, put a volt meter on the battery side of the coil and see how much it drops when cranking. A bad starter can cause this, but the problem is often cable internal corrosion and/or bad connections at the battery, starter solenoid, starter terminal, ground straps, etc.