Since you mentioned something about the transmission, another possibility is the trans neutral switch which ensures that the car must be in park in order to start it. Jiggle the trans stick in park and try it. If not successful, there is a terminal block (4 connectors with a black cover) near driver's fender side. If you jump the first and third terminals (the two with larger diameter wires), the starter solenoid will be energized, bypassing all the interlocks. Worth a try. If you only hear a click with this method, the solenoid/starter is definitely bad.

Good luck!

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Shane83SD