1998 Infiniti I30

Electrical problem
1998 Infiniti I30 Front Wheel Drive Automatic

My daughter's car will not turn over. Power to everything os fine. Starter, Alternator and Battery checks out fine. Neutral safety switch is fine. Turn the key. All lights and radio come on. Windows work. But car wont engage. No clicking. Nothing.
Had it towed to mechanic. When it got there. It cranked.
She drove it for three days. It did it again. Had it towed to mechanic. It wouldn't crank. They disconnected the positive battery cable for a few minutes. It cranked. And cranked twenty times in a row.

She drove it home. Set the alarm with the key fob and it re-cranked.I asked her to set the alarm and then enter and turn off the alarm using her key to open the driver's door instead of the key fob. She did this. And it will not crank.

Got any suggestions.
Jerry Pece
404-310-4216
Douglasville, GA. 30135