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Perform the shifter wiggle test, while turning the ignition key to start, to have the starter motor crank the engine as tomw suggested above in post 12 & let us know how it goes.
OK, check the wiring harness, wiring & electrical connector at the drivers side tranny connection point & make sure the tranny range switch is securely fastened, no loose, or missing fasteners. If all that looks ok, then move the range switch up to the top of your suspect list.
You have been jumping the 2 big posts on the silenoid. Have you tried applying 12volts to the hot side of the B+ posts to confirm the silenoid is working properly (i understand it was replaced). If that works then do a physical check of the switches at the brake pedal to make sure they are intack, and check to make sure the brake ligts are turning on.
tomb, the brake pedal is not involved if the transmission is an automatic, except to disable the interlock so the lever can be moved from the Park position with the brake pedal depressed.
As you say, if power is applied to the small terminal on the solenoid, and the starter engages, then the assumption can be made that the large cables, the starter and the solenoid are functional. I suspect that power is not being applied to the small terminal.
The switches, ignition, MLPS, and PATS(?) and the interconnecting wires are all that is left.
Power travels on a red/lt blue from ignition switch to IP fuse panel through fuse #24 10A out on red/lt blue to a jumper if no AntiTheft or starter interrupter relay if it has AntiTheft, to a jumper for automatic or clutch pedal switch for manual, out of the clutch pedal on a pink to the range selector (MLPS) in on pin 4, out on a red/lt blue - pin 1 - to the relay on the inner fender.
The starter interrupt relay is energized by the remote anti-theft personality(RAP) module. The wire from the RAP module is colored lt grn/ppl (light green/purple). The RAP
module, when denying starter power, sends power to the interrupt relay, opening the contact that passes power to the clutch pedal area.
If you jumper the red/lt blue wire connection to the wht/pink connection, you have bypassed said RAP and power should flow.
To check this stuff, get a test light, and plug into the bits following the flow as noted. In START, the light should light all the way along. When it doesn't, you've found the problem, hopefully.
tom