If the starter is not engaging after checking what you have already:

1. Neutral safety switch?

2. Bad starter solenoid?

When you turn the key to the position that would normally engage the starter are you getting 12v at the solenoid? If not I would suspect the neutral safety switch. Have you tried holding the key in the start position and moving the gear selector through it range to see if the starter engages? No voltage at the solenoid could also be a defective ignition switch.

If you have 12v at the solenoid in the start position it should close the contacts and cause the starter to engage. If you bypass the solenoid by jumping over it and the starter engages you have a bad solenoid. Jump it with something heavy like two screwdrivers. If the jumper does not cause it to engage then I would suspect a bad starter if you have previously verified a good ground on the starter. Those cables can have defective contact at either end or develop a high resistance at the point they are attached to the ends due to corrosion.

Good luck and let us know what you find out.

Randy