Vehicles now have a Neutral Safety switch(NSS)
If an automatic trans then there is a switch on the transmission, this switch must be depressed/closed for the 12volts from the key/ignition switch to pass to the starter motor, it is only depressed when trans is all the way into Park or Neutral.
Cable shifters can get out of adjustment, so Park is not "all the way in" so switch isn't closed, try starting in Neutral.
This is also the Reverse Light switch, so if Reverse lights are not working, look at the switch.
On Manual trans the NSS is on the clutch pedal push rod, when clutch pedal is pushed down all the way this switch is closed and 12volts can pass from key/ignition switch to starter motor.
This switch just clamps on to the push rod and floats on the rod.
When the key is turned it moves a slide bar in the ignition switch, this switch has 4 positions, ACC-OFF-RUN-START
Each position has it's own 12volt OUT wire, so ignition switch could also be the problem, but NSS or its wiring is the most likely cause.
Ignition switch-----------NSS----------------Starter solenoid/relay