Ok, the car would definatley have a theft deterrent in the key. However it's under the plastic and you likely don't see it. No worries because you aren't having a security issue. When there is a security problem, the injectors prime with key on, the car starts, then promptly stalls. Doesn't sounds like you are getting that at all.
Also with key on, the pump primes and stops running until the engine runs.
Have you checked for spark?