Hi HankM1942. Welcome to the forum. Have a test light ready for the next time the problem occurs. When it does, jump out and use it to measure battery voltage. Assuming it's ok, move the probe from the positive terminal to the other end of the cable where it attaches to the solenoid. Next, move the negative clip to the engine block, then to a paint-free ground bolt on the body. You're looking for the place where the test light is no longer nice and bright. When you find the first spot where the light is dim, you just passed the bad or corroded spot or loose connection.
Loose copper bolts on the solenoid are common but you would have caught that when you replaced it. Ford likes to use one of the large solenoid terminals as a convenient tie point for the vehicle's other electrical circuits. That's why a loose connection in the starter circuit there affects the whole vehicle.
Another common Ford problem is corroded battery cables but the corrosion is hidden under the insulation. This happens most often down by the starter where it doesn't affect the rest of the truck, just engine cranking, but it can happen to the other cables as well.
Caradiodoc
SPONSORED LINKS
Tuesday, August 10th, 2010 AT 2:00 PM