The officer never gave me a Miranda warning. Can I get my case dismissed?
No. The officer is supposed to give a warning of your right to remain silent and tell you that anything you say may be used against you in a court of law (your 5th Amendment rights) and that you have a right to consult an attorney, and if you can not afford one you have a right to have a lawyer appointed for you (your 6th Amendment rights) after s/he arrests you. Sometimes officers do not.
The only possible consequence of failing to advise a suspect of his Miranda rights is that the prosecution cannot use any of the suspect’s answers to questions asked by the police after the arrest. This has little or no application to DWI cases, because an officer can question a driver as much as he pleases while the driver sits in his car not under arrest. These questions are the first part of the officer’s investigation, long before the arrest. Because the driver is theoretically not under arrest, the officer can ask all the questions he wants without giving the Miranda warnings.
Of more consequence in most cases is the failure to advise you of the state's "implied consent" law, that is, your legal obligation to take a chemical test and the results if you refuse. This can impact the suspension of your license.