The factory alarm has a starter disable. You need to re-arm the factory alarm and then disarm the factory alarm. If you have an after-market it may not be properly integrated try this regardless. Lock the car using the key at either the driver's side or the passenger's side door. Wait for the Security LED on the dash to light up and then wait for it to start flashing (about 30-60 seconds). Now unlock the door with the key at either door or the trunk.
There is a switch mounted to the back of each lock cylinder and they wear out. Typically the passenger door lock and the trunk locks are used so infrequently that they work fine if the driver's side lock is no longer disabling the alarm.
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