I went through this with a friends F150, first we replaced the starter solenoid, then the starter, then the starter solenoid again and the positive battery cable as his had intermittent starts,starter would not disengage, finally I pulled off the starter and had it tested, The lady at Advance did not like how it sounded so I paid for a upgraded starter and installed that, no issues afterward, my suggestion if you can is to:
1. Check the battery charge if the truck does not start and see if it drained
2. As aforementioned check any modified or added wiring ( and battery cables for connection/ corrosion)
3. recheck the alternator, i had replaced one and after some issues (on another F-150) took it back to have it tested and it fried the testing machine.
4. last but not least check the starter, you never know..
5. recheck your radio wiring if you installed a radio, I shorted out a live wire not realizing it was live...
Hope this is a help.