Check to see if your battery connections are super clean, I had a very similar problem (although I wasn't in an accident though) where I would turn the key and the lights would come on and everything would seem fine until I turned the key to start it and the car would go dead, I thought I had some major problem (like you're thinking) and it turned out to be a simple matter of cleaning the battery connections to the point where they are shiny. I used an exacto blade and actually scraped them clean, since then no problems. I am wondering if in the accident you perhaps jogged the battery connections to a point where they don't have a good connection.
Let me know if that helped.