There is also an interlock to keep the starter from working unless: The car is in Park or Neutral (with an automatic transmission), or unless the clutch pedal is held down (with a manual transmission). That switch or its connector could be the problem. On my 97 the switch is on the front of the automatic transmission, down low. I dont know where it is on the manual transmissions. My guess would be; on the clutch mechanism under the dashboard.
And with the automatic transmission, you could try wiggling the shift lever - in case the shift linkage to the transmission is out of adjustment.