there is a lot of good information in the other posts, lets see if I can help put it all into perspective.
you've said the starter has been replaced and the cables are good and all it does is "click", also it push starts, so you must have a standard trans and we can rule out a mechanical problem with the engine.
It sounds like an electrical problem from the symptoms and with the starter already replaced that leaves the cables, wires and connectors, clutch switch and ignition switch.
There are only three basic circuits related to the starter in your truck
1. the positive circuit, (positive battery cable) which runs from battery positive to the large terminal on the starter motor
2. The ground circuit which runs from battery negative to the starter housing (this includes the negative battery cable, the engine block and the starter case)
3. the "crank circuit" which inludes the ignition switch and the clutch switch (on a manual transmission). this circuit runs from the battery positive (using the battery cable) and goes thru the harness to the ign switch then to the clutch switch and back out to the starter "S" terminal on the starter.
Do the easy stuff first, make sure the cables are tight - AT BOTH ENDS OF THE CABLES - at the battery and at the starter and engine block.
I suggest loosening the clamps and the bolts/nuts at the block and starter slightly and turning them back and forth a few times to breakup any corrosion, then tighten them.
Next make sure that none of the cables or wires are laying against a sharp edge, or the exhaust manifold.
Now, lets do a quick check of the starter, cables and solenoid.
With the truck in neutral and the emergency brake set (both these steps are critical for your safety!) use a jumper wire or test lead at the starter and connect the 'S' terminal (the smaller purple wire) to the terminal with the battery cable attatched. your are applying power the the solenoid the same way the ignition switch does.
If the engine cranks then the problem is in the "crank" circuit and the positive and negative circuits, starter and solenoid are ok. Next go under the dash and disconnect the clutch switch connector at the clutch pedal and put a paper clip or jumper wire between the purple wire and the yellow wire.
turn the ign to the "CRANK" position to start the truck. If it starts then replace the clutch switch assembly if it still won't start then the problem is the ign switch or a wire in the "crank" circuit which may be difficult to find.