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Here are the wiring schematics for your starter system. 1st pic is without anti-theft and the 2nd pic is with.
Now since you here the solenoid click I suspect that you are getting 12V on the T/R wire at the solenoid but go ahead and double check it anyway with your voltmeter and make sure you have 12V there with key in start position. If it is ok then take you a screw driver and short the battery positive side of the solenoid to the terminal where the T/R wire hooks up and see if starter engages and turns. If it doesn't then you have a cable or ground problem. If starter does not engage and turn when you do this hook the T/R wire back up and take your voltmeter and hook one end to the battery positive cable at the battery and the other end to starter terminal where positive cable hooks to it,you should read 12V. Then have someone turn ignition to start position and hold it there. You voltmeter should drop to less than 1V. This is checking the entire circuit from battery to starter, called voltage drop. If it does not drop below 1V then you have something wrong,either the cable from battery to solenoid,the solenoid,or the cable from solenoid to starter is bad.You can test each cable this way and the solenoid also. Just take your lead that is hooked at the starter and work you way back until you see the drop to less than 1V.
If this checks good then take the bolts out of the starter one at a time and look at the threads good. If they are black you may be loosing your ground from the starter to the block. Take a wire brush and clean the threads really good and reinstall and see if this cures your concern.
If this does not then take like a set of jumper cables and hook one end to battery negative cable and the other end to a good ground on the chassis and see if it cranks then,if so then your negative cable is bad.