I've had the same problem with two of my 123's. Both required the same repair which solved the starting problem. Assuming the battery is good and has enough current to turn the starter motor, and if you can jumper the starter with a screw driver from the purple wire connection and the starter engages then assume it works, then the battery has enough power to turn the starter. This tells you the high current side works. So next turn attention to the low current side of the circuit, ie the key ignition switch and the neutral safety switch. In my case the shifter was not completely allowing the shifting linkage to properly allow the neutral safety switch to dis-engage. The result was the car would not start by the key. The fix was replacing all bushings in the shifter and shift linkage arm. Cost about $8.00 from peachparts.