Are you positive the car has been turned completely off with the button? It can still be running if you walk out of the car with the keys in your hand. Don't mean to offend, but I've seen many people do this...
Also make sure the headlight switch is turned off and not in the on position (personally I don't even like the auto position).
Let me know about these 2 things and we can take it from there :)
Do you still fall under factory warranty? Just curious...
If the switch is off, the start button is completely off, and they stay on regardless then chances are either you've had a switch or relay go bad, or have a wire shorted out somewhere. A couple more questions.
Do you have an aftermarket alarm of any kind of the car?
Has it ever been in an accident?
Have you had any work performed recently?
The only other DIY suggestion I think I could offer at this point if you answer NO to all of those questions, is disconnect the negative battery terminal for about 2 minutes. Then hook it back up again and tell me what happens.
The tire pressure monitor couldn't have anything to do with it. This is something inside the wheel and completely unrelated. The Toyota Factory security shouldn't have anything to do with it.
The accident worries me, however. Funny things can pop up unexpectedly long after the accident. Actually, right now at this minute there is a 2007 Avalon I'm working on at work. A little more severe of a case, but you'll see where I'm going with this. They towed this car in, poor guy actually missed a flight to Tennessee for work because his car wouldn't start. Figured it was a dead battery, so he tried to jumpstart it. Still absolutely no power inside the car to ANYTHING so he towed it in to us. There are burned (like literally caught on fire and burned) wire harnesses all over the place. Investigated a little closer and found no VIN label on the fender, then looked at the front bumper reinforcement bar and found a parts sticker on it. He was in an accident in july of 2008. Well, the fusebox that bolts to that fender that was replaced had gotten cracked at the top of it. Slowly water leaked into a sealed portion of it due to the crack, and overnight it rained and shorted, setting harnesses on fire, resulting in his "dead battery" the next morning. Remember this all happened nearly 2 years after the initial accident, but was damage from the accident their body shop missed when doing the repair. His insurance company is covering it, luckily. Because there is close to $3000 in parts we've ordered to repair his car.
Either way, I'd highly recommend taking it into the dealership. Leave your negative battery terminal disconnected overnight so it doesn't kill the battery before you leave, but take it into the dealership. Because either 1)something has failed/shorted/gone awry and will be covered by warranty, or 2)something has failed/shorted/gone awry from the accident and your insurance company can issue an addendum to cover it that way. Either way you're in good shape, it's just more of an inconvenience than anything, unfortunately.
Best of luck to you! :)
Edit: Your battery is in the trunk in the back corner, on the passenger side (right side) under the little cover.