Why won't 2001 Toyota Solara start after a small accident?

There could be hundreds of reasons although the choices might have been narrowed a little if you'd specified the type accident and specific damages. Possibilities range from something as simple as a damaged battery or battery cable (if you don't even get lights on the dash when turning on the key it's a possibility) to a damaged alarm system (starter lockout) or even a damaged transponder in your ignition key. There are plenty of things in between. When you make an appointment with the insurance adjuster tell them the car hasn't started since the incident. They'll arrange to have the vehicle towed to a repair shop (that you specify if you have a favorite) for the accident repair and 'won't start' diagnosis. Cheers