If the mechanic fixed it before in the electrical distribution box, I would start back there. Since you've already cleaned the starter relay there is also the start diode in that same box to be checked. Doesn't take much corrosion on these small connections to upset current flow. When cycling the key, you should be able to hear/feel that starter relay cycling. With suspected neutral safety switch, I would attempt to start it with the shift lever in every position. I agree with MR. P on using a voltmeter/ohmmeter. A little troubleshooting would have saved you a few hundred in parts so far. If you have a meter then we can definitely go into more depth on testing.