Wiring diagram starter will not turn over but will if jumped at starter

This sounds like the starter solenoid isn't getting enough power. Jumping the solenoid is you simply bypassing it. Go back to basics. I may suggest things here you have already done but it helps to treat this as a simple check list.
- Check the fuse, sometimes the fix is that easy.
- Check the relay for the starter motor. It should click when the key is turned sending power to the solenoid.
- Check the voltage supply at the small wires at the solenoid. Using a multi meter set to DC Volts you should get around 12 volts when you turn the key. You might need a helper to do this.

Note the diagram. Make sure battery has a full charge and connections all good. For starter motor testing, pull starter relay, use jumper wire on switch side of relay, left side in diagram, cavities for terminals 87 and 30. The starter motor should crank the engine. Even w/o the key. If you try that, make sure transmission is in park or neutral and parking brake is set. Vehicle can't move. When you jump the relay, if key is in on position, just where the dash lights come on, depending on the problem, the vehicle may start and run? By jumping the switch side of relay, you bypass the control side of relay, right side in diagram. I haven't looked up your security system, some fords, the security system is starter motor disable among other components. good luck

Do you know what a wiring diagram is ? How to use a DMM - digital multi-meter to diagnose automotive electrical circuit's ? Looking at a wiring diagram to see what all is involved in the starter circuit , main battery cables , park neutral safety switch , starter relay etc.. Find video's on youtube . Do you have a manual or automatic trans. ? The purple wire get's B+ voltage from the starter relay in the underhood fuse / relay box .

How to voltage drop test starter motor circuit
When your car wont crank or start part 3 How to check relays fuses...

If it worked a few times, the wiring is probably correct. Your symptom indicates a low battery or bad connection. Clean and tighten battery terminals as well as where the cables connect to the engine and starter. Try jump starting. If it jump starts, check the voltage at the battety with the truck running. Voltage should be at least 14vdc. If not, remove the alternator and have it tested at your local parts store.

Here is a link to the wiring diagrams, look it up. http://bbbind.com/free_tsb.html

Yes there is a starter relay in the wiring diagram.
The yellow and lite blue wire goes from the starter solenoid to the relay. There is a yellow wire from the relay to a 30amp fuse. The key switch powers thru the neutral safety switch and then powers the relay on.

Did you check the starter and starter relay. If the starter is failing it will require more voltage than usual to turn over and start the truck. Heat soaking can also be a problem. Check the wiring to the starter and any wiring you reconnected when you replaced the alternator.

First start by jump starting. If jump start works, you have a bad battery. If it does not, then starter is bad.

I dont have a diagram, but that recently happened to me on a 02 GMC Envoy. The problem was that 2 of the wires connected to the starter were making contact with eachother. Make sure none of them are touching. Hope this helps. Good luck

if by bypass you mean the ignition switch. jump it at the relay, find the starter relay the relay should have a diagram on the side and numbered posts on the bottom with a jumper wire you can jump the post in the power distribution. look at the diagram there should be a switch which shows normally open you need to jump the posts that would close this switch and this will jump you starter make sure you key is on to start the vehicle. hope this helps some