My 05 titan wouldn't start

I have a 2005 titan SE 5.6,i recently bought it for $4000 from another person.he stated that he change the engine with about 98000 miles on it.he changed the alternator as well. Everything was working just fine that same day i bought.the next day i tried to take it to work but it wouldn't start.everything would work perfectly,all the lights,the radio.but when i opened the switch you would hear 1 click sound and would not crank.my battery is good tho.so i took it to the mechanic and got a new starter.my truck would start perfectly,no issue.i do have the engine service light on tho.since i bout it it was already on.so anyways,i drove my truck for 2 days to work without any issues.then out of nowhere it started heating up,so i stopped for 30 minutes for it to cool down the crank my truck again and drove it about 2 miles without it over heating again.i took it to the mechanic again.(i forgot to mention that he was gonna change the throttle body which he said i needed.i still haven't changed it.)so,today i took my truck to work and when i got off,my truck did not start again.but this time when i turned the switch on, there was not clicking sound at all.but everything works fine.can someone explaine whats goin on with my baby.please and thank you