I had a similar issue with my car recently, and I found that if i messed with the wires under the dash, the car would then start. I found one of the connections had become slightly loose on the passkey system. The security light would continually blink while i attempted to start it, i'd leave, come back, and it'd start. I cleaned and secured the connector. The car has started fine the past 2 days, since i fixed the connector.
I'd check the starter solenoid first. Mine wasn't getting power, which lead me under the dash.