Before running off the autoparts store to buy Ford parts, I suggest there is about a 90 percent chance your solenoid is just peachy dandy fine. At least do some basic troubleshooting before deciding to replace any parts!
FIRST get a multimeter... put it in VDC scale. Open up your right hand switch gear housing (two 5mm phillips head screws) and turn your key on. Put the BLACK (neg) probe on a frame ground and the RED (pos) probe on the wire going into your kill switch. Should be 12 VDC. If there is no voltage here, then the problem is between the fuse box, OR your igntion switch. It is probably going to show 12VDC.
With the kill switch ON (and the key still on), move your RED probe to the wire coming OUT of the kill switch. If you have voltage, then move on... otherwise check the killswitch being ON. Otherwise, you have a bad killswitch connection.
If you have voltage coming OUT of the kill switch, note there is a wire going to the back of the button (soldered to a contact plate. Check voltage here. You could have a bad solder joint but most likely there WILL be voltage at this point.
Last, there is a wire coming off the button so that when the button is depressed, the power goes through the start button and to this wire. This wire becomes the trigger for your solenoid. PUSH THE START BUTTON with the igntion ON and check for power. If you have some, then the connector between the switchgear and main wiring harness will need to be checked (it can be loose) but most often is the button contact. It can be removed and cleaned with steel wool or emory board... less is better as you remove conductive material with a lot of cleaning. You can also spray it with contact cleaner. I don't like to use dielectic grease becuase it draws grit.
The problem is likely in the button contact OR the connector between the switchgear and harness along the right side of the steering neck...
Heck, you could try finding voltage on the trigger when the button is pushed first (probably a good idea) because if there is 12VDC on the solenoid where the small trigger wire comes in when the button is pushed with the igntion on, that would tell you the solenoid is bad hehe but I doubt the solenoid is bad and feel it is more like somewhere on the voltage path the trigger wiring follows.