[cjb15]

Here are a few old school things to try. The little wire on the solenoid on top of the starter is the wire that makes the solenoid engage the starter. When the key is turned to the run position you should have 12 volts at that wire. If you do then you still have problem with your starter or solenoid. If not then you have to work your way back through the wiring system, switches, and relays that may be in the system.
Another thing to try, there is a switch in the gear selector lever to make sure you only start in neutral or park (if a manual there is an equivalent clutch pedal switch). You should try jiggling the lever in park and/or neutral to see if that fixes it.
Let us know what you find.