The security system will prevent the starter from working until the system is reset. To reset the system, lock and unlock the driver's and passenger side doors with the key. One door is usually OK, but I've had problems with my driver's side not turning off the alarm, and having to use the passenger side lock to reset it.
If the problem persists, you can by-pass the security system here:
http://www.toyota-supra.info/forums/...rm-system.html