Traffic accident

The very fact that you were hit from behind while driving gives you the ability to make a claim against the driver for negligence.  Did the police cite the driver for any violations at all?  Regardless of the officer's report, you may file a lawsuit for the property damages based on the fact that the driver was following too closely and failed to maintain his vehicle in a reasonably manner.  I suggest that you go to the hospital to determine whether you have any serious injuries as you may be able to claim pain and suffering damages and property damages.  You need to hire a lawyer to place the other driver's insurance carrier on notice and then file suit if there is no settlement.

If the other driver was negligent--or unreasonably careless--he would be liable and you should be able to collect in a court case. Certainly, DUI/DWI would show negligence, but so would driving while too fatigued or falling asleep at the wheel. (Also speeding, texting or phoning while driving, bending down to change the radio and not paying attention, having bad brakes, etc.) While it's not a given that the rear driver in this sort of crash was at fault, it most likely is the case, and there are many ways to show negligence.

Before suing though: is it worth it? First, how much non-compensated (i.e not paid by insurance) damage or costs have you suffered? If it's not at least a few thousand dollars (or long lasting or permanent disability or scarring), it's probably not worth it. Also, if you win, does it appear the other driver could pay, whether by insurance, income, or assets? It's a hollow victory to sue, win, and still not be paid.