Probably a bad key switch, the starter needs voltage from the switch to the solenoid to engage so start there.
You might also want to look at the starter, sometimes something can get lodged down there and bridge the connection.
The starter is on the side of the engine at the bottom.
the solenoid on that year ford starter is on top of the starter itself. that starter is used on a wide variety of ford products.
either the starter is worn out and needs rebuilding, or the battery is bad
could be right in front of the battery - that's where it is on my 89
Most commonly, it's the starter or the starter was wired wrong when it was installed. More rarely, it can also be the keyswitch or even a bad gear on the flex-plate.
it is located under the engine on the right side of the engine. crawl under the right front wheel and you will see the starter motor and the associated wiring.
The engine has to be removed.
the starter motor on just about any engine is very close to the crankshaft. the easiest way to find it is to follow the wires of the ignition system (usually yellow, sometimes black, it depends) the ignition system is directly connected to the starter.
The starter in your E350 could be going bad. If the sensor or wiring is faulty, you will not get enough power.
check the battery voltage (14 volts and above) and check the solenoid
If the red wire is a smaller wire to the starter motor, then its a faulty ignition switch. If its the large wire to the starter, then its meant to be live all the time. hope this helps
Large plug in back of heads