Car start on any shifter position

I have a 1995 Cutlass supreme, OBD2 converted with a 97 Cutlass engine, tranny, computer and wiring. When I finished the conversion, everything work fine except for one thing, engine won't crank with the key. It crank and start, and work fine when I jump the starter solenoide, but nothing happen from the key "start" position. I brought the car at a GM dealer to have the key reprogrammed, but the tehcnician simply by-pass the security system. Few weeks ago, the police ask me an inspection for the car and they found that it start at any shifter position. I tchek the neutral safety switch and it's OK, but I could start the car even with the switch unpluged. I don't know if this problem was present before the security system was bypassed, but I think the problem come from this "backyard repair". Am I wright? How can I test that? I can't put the car back on road before this issue being fixed.