I'm with chichi and dustybird on this one.
Since the security light is coming on, I'd guess it's the passlock.
That happened to my '01 LS, where the security light would come on sometimes when I was driving and then one day after about a month of that it just wouldn't start. All of the electronics worked so I knew my battery wasn't dead, but the car wouldn't even attempt to turn over and the security light was flashing alternately with the battery light.
That was years before I knew about this forum, and ended up having my car towed to a dealership where they replaced the BCM (it was under warranty thankfully).

Like dustybird said though, if the starter is clicking then it is NOT the passlock. Clicking starter could be a bad battery, but I would think more likely it would be either a bad starter switch/solenoid, or a bad starter.
When the passlock kicks in, it will keep everything on, but disable the starter and flash the security light on the dash.

Good luck, and keep us posted.

-Riggs.