Don't have an 03, but a little more info on why you don't think its armed ? No confirming chirp ? No flashing parking lights on the X ? Horn not blasting ?
Solutions??
Alarm set to silent mode.
Bad battery in the remote ? Try the second remote.
If you are just testing it by arming it and opening it through an open window, it takes a minute or two before it fully arms before it will honk.
As a final test (on the remote end of things), leave the window open, lock it with your key, wait a minute, then open the door from the inside. (it should sound)
**note, if the remote isn't working, you'll have to dissarm by unlocking with the key, but I'm not sure if it will turn it off immediately, or when the alarm resets after sounding.