Dead starter?
Did you follow the starter alignment instructions when you replaced the starter? Are you getting oil on the Bendix? That could cause the starter gear to engage slowly. It is possible that the replacment starter has a problem. Also, if the previous starter had the same problem it could have damaged the gear on the flex plate.
Does it turn over? Could be a bad starter solenoid Could be a bad starter Check wiring
Maybe you have a problem in your main wiring harness. No fun.. Could also be an electrical sensor.
The starter or battery could be weak. The weakness will cause the starter to turn too slowly to start the truck.
It is most likely the neutral safety switch needs to be replaced, which can be a little expensive. However you can bypass it and install a kill switch, the problem with this is if the vehicle is gear it will lurch forward if you start it
COULD BE THE CRANK POSITION SENSOR
It could be a starter problem....can you tell where the click is coming from? is it the started clicking, or a relay clicking?
If you have just replaced this starter then you probably have it hooked up incorrectly. If it is still the same old starter, then it has shorted out inside and needs to be replaced.
check starter
power, ie battery, then starter, then spark, then fuel
It can be a defective starter assembly that causes this problem. There are two parts to a starter assembly: the starter motor and the starter solenoid. The offending culprit is usually the starter solenoid, and it should be replaced.