Do you know for sure that they had no insurance? If they don't you are probably better off getting the car fixed under your collision coverage and go after them for your deductible. If you don't know if they have coverage, consult a lawyer in your area.
You certainly have a civil claim and there may well be a criminal case against the drunk driver as well. First you will need to confirm that he/she truly has no insurance. If it appears that the other driver, in fact, has no insurance, then you will want to check you insurance policy to see if you have uninsured motorist coverage that could cover the cost of damages. If you have UIM, then your carrier will likely take legal action against the fault driver to try to recover their costs. If you don't have UIM, then you may want to consider filing a civil action against the fault driver depending on the type of personal assets that he appears to have available.