91 F-250 Diesel won't start

I know the batteries are good cause they both have 12.5 volts.I also cleaned the battery terminals good with a wire brush and sprayed battery protector on them.I know the starter is good cause I took it off and auto zone tested it and it tested good.I replaced the solenoid on the fenderwell thinking it was that and still won't start.Here is the clincher,it will crank and start if I connect my remote starter switch across the solenoid on the fenderwell.What is left the neutral safety switch?Well I already tried jumping the two wires across the neutral safety switch that are red with a blue line and it still will not crank and start.So I am about to pull what little hair I have left out on this one so any help would be much appreciated and my wife will thank you too cause even though I know she loves me alot I think she would prefer if I had some hair for a little while longer cause I am just 40 years old lol!

I think your fender-mounted solenoid has three terminals - two will be large, and the other one smaller. Connections should be:

First large terminal: has heavy cable arriving from battery positive terminal.
Second large terminal: has equally heavy cable running to starter motor.
Smaller terminal: has thin red/light blue wire arriving from neutral safety switch.

I'm not sure which two wires you were bridging, because there are two ways to bridge the solenoid:

1. Bridging the two heavy wires (with an equally heavy wire or a heavy screwdriver, etc.) will cause the engine to crank and run, but doesn't help in giving any indication of what is wrong with the starter circuit (because it bypasses the solenoid).

2. Bridging the first large terminal (fed from battery positive terminal) to the small terminal should cause the solenoid to energise, and the engine should crank and run.

The first method only tells you that your starter motor is healthy, but you already know that.

The second method tells you that the fender-mounted solenoid is healthy but also indicates that 12V is not arriving at the solenoid coil terminal via the normal route, which as you already know is: ignition switch 'Start' contacts - to neutral safety switch - to fender-mounted solenoid coil terminal (that's the smaller of the three terminals, to which the red/light blue wire connects).

You can verify that with a multimeter or a 12V test lamp - the solenoid coil terminal should have 12V when the ignition switch is turned to the 'Start' position. If the 12V is indeed missing then you'll need to trace back through the circuit, looking for an open-circuit or a bad connector (loose, dirty, or corroded). If that's the original ignition switch then it's possible that the 'Start' contacts have failed. Tracing the voltage is awkward because you only have 12V when the ignition switch is held at the Start position, so therefore it's much easier to leave the ignition switched off and find the fault by continuity testing instead, using a multimeter on its resistance range.

Thank you Selectron for your suggestion it was a faulty ignition switch.I replaced it with a new one from auto zone for just $11 and it started right up.So if anyone ever has the same problem I was having it is usually an easy fix if you are mechanically inclined.The starting circuit includes the following,the battery(batteries),the starter,the solenoid,the neutral safety switch and the ignition switch which is located on the steering column.About the only other thing that can give problems with the starting cirtuit is corroded or faulty connections.So maybe this might help someone else.

If only all repairs were so cheap and easy eh. Thanks for letting us know.