Miranda rights only refer to post arrest questioning by the police. If you were questioned about your offense without the warnings after your arrest you can get your answers thrown out. That doesn't mean the case will be dismissed.
As Mr. Karnan notes in his response, a Miranda violation only addresses the admissibility of the statements that are made in response to "un-warned" questioning by police in a custodial setting. Depending upon the context in which the court personnel talked with you, statements you made to them may or may not be admissible under a sixth amendment analysis. The determination on admissibility of either set of statements is heavily fact-determinative and you should consult an attorney within the protections of the attorney-client relationship to get the most-correct answer to your questions.
Whether or not your case is dismissed is rarely determined solely by the admissibility of statements you have made, unless those statements are the only evidence against you. However, if the statemens are the foundation of the government's case against you, their admissibility will be a key factor considered by the prosecutors in determining whether or not to proceed with your case.