The starter relay, or solenoid, itself may be bad if you checked the fuse but not the relay itself. Seems like you have done all the right things, the battery of course, all that. The cable to the starter comes to mind. There is a way, if you have a manual transmission, be sure it's in neutral, make sure the parking brake is on, chock all wheels and take a jumper cable from the positive terminal on the battery directly to the starter cable lug, key in "on' position, see what happens.
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