From the sounds of it, the damages are not that much. If so, you should probably file an action in small claims. The insurer usually will not want to spend the money on sending a lawyer to small claims for most of the day to defend if the amount is small. They will probably pay you.
If the amount is large then you probably need to consult an attorney to file for you.
If no one was injured, you may be able to file this in a small claims court.
*PLEASE READ THIS BEFORE YOU COMMENT, EMAIL OR CONTACT ME. I am only licensed in Washington. Answering this question does not create an attorney-client relationship. This answer does not constitute legal advice.
The other driver's insurance company will delay for as long as you allow them to do that. File in small claims court a.s.a.p., and force their hand to act with haste, one way or another.
I agree with the small claims court advise of the other lawyers if you were not injured in the accident. However, if you go to small claims court, make sure that you bring a claim for everything, because if you were hurt, and didn't bring that up in the small claims court, then you may have forfeited any claim for injuries.
If you were injured (hopefully you were not!) then contact a personal injury lawyer.
If the insurance compnay refuses to communicate with you or tries to bully you beyond a legitimate defense, you can contact the office of the insurance commissioner as a further resource.
Sign up to receive a 3-part series of useful information and advice about personal injury law.