Things to check, in this order:
1) Battery has proper voltage. At below a certain level you won't even get the distinctive "click click click click" of a dead batter. It'll just turn off the interior lights.
2) If you are positive that your battery is fine. Turn off the ignition. Close all the car doors. Then with the Key, turn the door lock to the left (to lock it). Check to make sure it locked. Then unlock the door, WITH THE KEY, and try the ignition again.
No sounds at all is distinctive of the Stock Alarm System's ignition kill feature.