A claim for ineffective assistance of counsel (which would be based on the advice given that led to your guilty plea) can be raised in a petition for writ of habeas corpus. But, such a petition can only be raised if you are in custody or still suffering the effects of the conviction, so I wonder if you are suffering under such a burden considering your conviction was for DWI.
You should talk with a lawyer who does habeas corpus applications to see what they think. The DWI does sound a little tough for the STate to make. What evidence did they have to support driving or being in control of the vehicle? Surely there has to be more to this for the State to have even taken the charges in the first place.
Although I have answered the question to try to help you, you should consult with a lawyer in your area in person on the matter. In addition, my answer does not establish an attorney-client relationship between us.