I have a 01 f250, I've only had it a couple of months. It has 300k miles on it and has its share of problems.
I knew that going in and I just bought it for a work truck around the farm and honestly I don't expect it to work perfectly. But since I have had it there are times where it will not crank, it will only click under the dash and then a second click under the hood. It will do that in the mornings a lot and by the afternoon it will crank. I found that jumping the 2 larger wires on the starter solenoid bypasses the problem and it will turn over and crank. So I replaced the solenoid thinking that was the problem, but it still does the same thing. I know the batteries are good, but other than that I am up for suggestions.

 

If it is an automatic, did you try shifting into neutral before starting?

Automatic transmission? It could be the transmission range sensor or dirty electrical connection to sensor.

Standard Trans? It could be the clutch pedal safety switch.

 

Nope, I don't think so. If there is a click, that would be the starter solenoid engaging. It could be a bad solenoid, connection, or a starter headed south.

 

It is an automatic. I tried it again, now I'm thinking that the 2nd click I'm hearing happens before I ever turn the key forward to crank it so maybe it's not the solenoid like I originally thought. I have tried shifting to neutral which has worked occasionally, but other times it doesn't, and since it will crank sometimes anyway I don't know if that is a coincidence or not. I've also tried wiggling the shifter in neutral and park, and shift multiple times to see if it would help. If it is a problem with the neutral safety switch where is it and how do I check it?

 

Yes, that is what I was thinking. The Neutral Safety switch is the Trans Range Sensor located on the side of the trans where the shift cable attaches. You will see the electrical connector.

 

It is a simple electrical circuit for the starter. Here is a link to the wiring diagram: http://www.revbase.com/BBBMotor/Wd/DownloadPdf?id=28952

With the connector still plugged into the trans range sensor, you can check for continuity between the db/og & tn/rd wires. These wires will be connected when the range sensor is in P or N. If there is no continuity in P or N then sensor is bad or poor connection at the connector.

If you feel that the range sensor is operating as it should, then check that the db/og wire is getting +12v when ignition key is in start position. If not, then check ignition switch (not the key cylinder, rather the electrical switch)

Since you have already replaced the solenoid and confirmed solenoid to starter is okay, it has to be either the ignition switch or the trans range sensor or wiring connections. You can see in the diagram that there are several inline connections that should be inspected if all else tested to be good.