Lincoln Navigator

If you have a slow crank check battery condition first. Make sure terminals are on tight and free of corrosion. Have a load test done. If battery passes the load test then do a cranking test. Voltage should not be lower then 9 volts. If it is, a voltage drop of the positive cable and ground cable should be done to check for high resistance in the cables. If that is ok then your starter motor will most likely be the problem.

If they bench tested the starter, to be honest with you, I do not trust that type of testing. The reason is once you have the starter out the vehicle it is not trying to turn over the engine. Now the gear spins free and someone could assume that the starter was fine? Here is a procedure to do a voltage drop test to verify that there is no high resistance in the cables. All you need is a good voltmeter to do this tests. If you are willing to try it here are the directions. As for the switch I am not familiar with that term? But definately have the voltage drop test done. You may even need to go to an automotive elctrician specialist for this if they actually can not figure this out? But that is your starting point now to verify if you have bad cables or a bad starter. Once the engine starts does it run ok? Let me know?

STARTER MOTOR - VOLTAGE DROP TEST

WARNING: When servicing the starter motor or performing other underhood work in the vicinity of the starter motor, be aware that the heavy gauge battery input lead at the starter solenoid is "electrically hot" at all times.

CAUTION: A protective cap or boot is provided over the battery input terminal on all vehicle lines and must be installed after servicing. Be sure to disconnect the battery ground cable before servicing the starter motor.

Always make the Rotunda 73 Digital Multimeter connections at the component terminal rather than at the wiring end connector. Making a connection at the wiring end connector could result in false readings because the meter will not pick up a high resistance between the wiring connector and the component.

Starter Motor - Motor Feed Circuit

Make sure the battery is fully charged. Refer to Charging Systems.
Disconnect the inertia fuel shutoff (IFS) switch.
Connect a remote starter switch between the starter solenoid S-terminal and the battery positive (+) terminal.

Connect the Rotunda 73 Digital Multimeter positive lead to the battery positive (+) post. Connect negative lead to the starter solenoid M-terminal.
Engage the remote starter switch. Read and record the voltage. The voltage reading should be 0.5 volt or less.
If the voltage reading is 0.5 volt or less, go to the Starter Motor - Motor Ground Circuit Component Test

If the voltage reading is greater than 0.5 volt, indicating excessive resistance, move the Rotunda 73 Digital Multimeter negative lead to the starter solenoid B-terminal and repeat the test. If the voltage reading at the B-terminal is lower than 0.5 volt, the concern is either in the connections at the starter solenoid or in the solenoid contacts.
Remove the cables from solenoid B-, S- and M-terminals. Clean the cables and connections and reinstall the cables to the correct terminals. Repeat Steps 3 through 6. If the voltage drop reading is still greater than 0.5 volt when checked at the M-terminal or less than 0.5 volt when checked at the B-terminal, the concern is in the solenoid contacts. Install a new starter motor.
If the voltage reading taken at the solenoid B-terminal is still greater than 0.5 volt after cleaning the cables and connections at the solenoid, the concern is either in the positive (+) battery cable connection or in the positive battery cable itself.
By moving the Rotunda 73 Digital Multimeter negative lead toward the battery and checking each mechanical connection point, the excessive voltage drop can be located. When the high reading disappears, the last mechanical point that was checked is the concern. Repair or install a new connection as required.
Starter Motor - Motor Ground Circuit

A slow cranking condition can be caused by resistance in the ground or return portion of the cranking circuit. Check the voltage drop in the ground circuit as follows:

Disconnect the inertia fuel shutoff switch.
Connect a remote starter switch between the starter solenoid S-terminal and the battery positive (+) terminal.

Connect the Rotunda 73 Digital Multimeter positive lead to the starter motor housing (the connection must be clean and free of rust or grease). Connect the negative lead to the negative (-) battery terminal.
Engage the remote starter switch and crank the engine. Read and record the voltage reading. The reading should be 0.2 volt or less.
If the voltage drop is more than 0.2 volt, clean the negative cable connections at the battery and body connections, and retest.
If the voltage drop is greater than 0.2 volt, determine which way the current is flowing in the cable. Connect the Rotunda 73 Digital Multimeter positive lead to the end of the cable nearest battery positive.
Connect the multimeter negative lead to the terminal at the other end of the cable.
Crank the engine and observe the voltage reading. The voltage reading should be 0.2 volt or lower. If the voltage drop is too high, clean the terminal ends. Retest, and if still high, install a new cable. If the voltage reading is less than 0.2 volt and the engine still cranks slowly, install a new starter motor.

I believe it is going to be between your battery cables or starter. That is why it is important to do the voltage drop test. In my experiance, I have had issues with both at sometime or another on my personal vehicles. Once My ground cable was actually broken off. The only thing grounding it was the small ground strap on top. Put a new ground cable and starting issue solved. 2 years later I started having the same problem again with the slow crank that it just would not start at times? It seemed like I had a bad battery but it was good. Ended up being a bad starter this time. When you do a voltage drop test on the cables, you are actually checking the whole cable for high resistance. Sometimes there may be no corrosion at the terminals but at the other end there could be. Especially if you happen to wash your engine from time to time. It causes problems in the long run with corrosion building up anywhere in the cables or electrical connections. So if you can have that test down it should narrow it down. It just may be a faulty starter but you still may want to verify the cables are good. Good luck and let me know what happenes.