Jumpering a voltmeter across the "coil activating" terminals during starting will tell you if the solenoid coil is getting power...which excludes starter switch, safety switch, and wiring if present. Jumpering across the solenoid with a pair of common pliers, (my usual method) will test the solenoid contacts.
Moving the Range Lever back and forth, changing nothing else will identify the safety switch as the culprit. My 1988 3910, bought a couple of years ago with 900 hours had such a problem as I could wiggle the range switch and when I found the sweet spot the tractor would light off immediately. Recalling, and somewhat vague, the problem was the same as "Birdhunter's". I bought a new switch and installed it and it helped but didn't give me 100% reliability.
In investigating the actual depression lever to switch contact, I found that the lever wasn't pushing the ball bearing down far enough. I installed a flat washer somewhere in there and that increased the depth of the lever's penetration such that it was adequate to cause the switch to close reliably.
Don't remember all the little details, but my problem was that the Range Lever wasn't pushing down on the switch hard enough. In summary, you may be able to fix your problem as I did and save the cost of a new switch, or may purchase a new switch and it fix it, or you may have to do as I did and if you buy a new switch and it doesn't work, shim it with a flat washer..or two...forgot where I put the shim. Good luck.
