Automatics have an NSS(Neutral Safety Switch) that the solenoid power must pass thru to activate the starter motor, it only passes power when trans is in Park or Neutral.
If an auto then try shifting into Neutral to start.
NSS is near the transmission linkage, it also does the reverse lights.
Manuals have a Clutch Switch, same thing, starter will not acivate unless clutch pedal is in all the way.
This switch is on the Master Cylinder pushrod under the dash.
Battery---------key----------NSS/Clutch switch-------------starter solenoid
Starter tested OK???
There is a smaller terminal on the starter motor solenoid, that is the activation terminal, if you apply 12v there the solenoid will close and pass the battery power to the starter motor.
If the battery cable to the starter motor is bad then motor won't get enough amps to turn, often lights will dim if this is the case.
But that is not always a sign, some lights dim when key is in START position on purpose, their power is cut to give all battery power to the starter motor.