There are two solenoids, the slave and the starter.
The slave is typically at the front top left of the engine.
To test either solenoid do this. *****remove the key from the ignition******!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! no key for this test!!!!!!
get a two connection momentary toggle switch connect two 12 guage wires (~24 inches long) one to each terminal and connect a alligator clip one to each wire or buy a remote starter (from a local auto store)
Connect one lead to a battery + or on the slave solenoid to the big terminal with 12 volts present all the time. connect the other lead to the yellow with red stripe. Activate switch. See what happens.
On the starter solenoid, connect one lead to Battery + or the large stud with the battery wire connected to it, connect the other lead to the small post with the yellow with red stripe, activate the switch, What happens?
If nothing happens but you hear a click form either solenoid, do this.
*****use extreme caution********* I repeat *****use extreme caution*********
On the slave solenoid, connect one lead each to the two top large terminals. ACTIVATE THE SWITCH FOR A SECOND OR TWO ONLY!!!!!!
THIS IS A HIGH CURRENT CONDITION AND COULD MELT THE WIRES IF DONE FOR AN EXTENDED PERIOD OF TIME.
This will bypass the solenoid, What happens?
If the starter does not work at this point then either the starter solenoid is defective or the starter.
remove starter and repair.......