Ok the first time I replaced the starter, the starter was just bad. Kinda like your situation. I went to the mall. When I came out truck would not start. Would not click, wouldn't do nothing. I had the truck towed home. The next morning off to the parts store for a new starter. Problem solved, the second time was the little wire on the starter kept coming loose. Ending up with the hole for the screw that holds the wire tight to the starter becoming stripped out. So lifetime warranty I replaced the starter for free. Then again for some reason that little bolt would not stay tight. So once again I replaced the starter again lifetime warranty. But this time I put a nut and bolt in place of that little screw. I put loc tite on that little nut and bolt. Since then I have not had a problem.
Now the mounting bolts the two times I had to replace the starter with the an aftermarket one. I found the bolts loose that held the starter in place. So the last time I replaced it I put loc tite on the bolts. Like I already said the bolts are still tight to this day.
Also if you have a 2002 F-250 and the starter goes out and you can't find the 2002 starter. You can use the older starter that requires three bolts to hold it in place. Just go to the hardware store and get a grade 8 bolt that is the same threads and length of the original starter bolts. The 2002 7.3L psd has the third bolt hole there. But the 2002 starter from the factory is a high torque starter and only required 2 bolts.