Make sure battery has a full charge and connections good. The picture is a fender mounted starter relay. For testing, make sure tranny is in park or neutral and functional parking brake is set, with this testing your bypassing everything, so it's important the vehicle can't move. I don't know what testing you have done?
Use a screwdriver shank across the two large brass looking studs in the picture, the starter motor should crank the engine, you don't even need to use the key. You may have already tried this, I don't know? At the least, you'll know the starter motor will crank the engine. One of the smaller wires, the feed, crank position, ignition switch. My wiring info for your model year isn't great.