When I have that problem its usually a loose battery cable attachment to the battery post. I won't admit it out loud, but I once pulled my motor out of the car because I thought I had cooked a starter when really all I needed to do was tighten that one bolt

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Take a battery cable and jump across + battery to the starter (in neutral of course) see if the starter turns over. Maybe a pain in the ass cause I think those solenoids are on the starter themselves.