I think Truckernix has the right idea, but backwards. The resistor bypass wire is missing or not hooked up, and the coil is not receiving any voltage untill you release the key. Verify this with a voltmeter or test light. Key on engine off, coil should have 12 volts (positive side), now crank engine. Does coil have voltage while cranking? If not, run a wire from the R terminal on the starter to coil positive.
