My F150 has had this problem for a few years, but now it happens a lot. The truck sits during the week. When I go to start it on the weekend, the fuel pump powers up, dash buzzers sound, but nothing from the starter. Sometimes if I hold the key in the start position, it'll fire up. Now, no matter how long I hold the key to start, nothing happens, just a clunk when I release the key. I had my wife hold the key while I tapped the starter. No luck, but I now know the clunk is coming from under the passenger side dashboard.
I happened to charge the battery up and when the battery is at full charge, it fires up without a problem. Any ideas as to what the problem is? To me it sound like corrosion between contacts, when there's enough power to jump the corrosion, it starts. I'm looking to sell it and want to fix it before it goes.
Thanks

 

Check the starter relay located under the hood on the passenger side. It should be mounted either on the firewall or the inside of the fender panel.
If the relay is OK, then the starter solenoid contacts may be burned in which case the starter must be pulled and either rebuilt or replaced.

 

a guy at work had a clunk every time he went to start it he cleaned all connection,ground to block and he took out the starter cleaned around their and it fixed his.