A couple years ago I steam cleaned my '83 TD engine and water got in the starter. I didn't know it at the time but, 3 months later the starter began to hang up. When I took it apart the solenoid was rusted and would not push the starter gear to engage the flywheel. My starter was 15 years old so I replaced it.
If you can remove the solenoid, clean and lubricate the piston and pivots. You may need an impact wrench to remove the 2 solenoid screws.
Also, don't forget about the neutral safety switch on an automatic tranny. Sometimes a faulty/misadjusted switch will disable the starter. In this case though the starter will not turn at all.