They didn't read me my Miranda Rights. Can I get the charges dismissed?

Probably not since Miranda Rights apply only after you have been arrested.  Any statements that you have made that could be incriminating can be used against you in court.  But, any statements you make between the times you are handcuffed and read your Miranda Rights cannot be used against you.  If it happens to be that the case against you is only based on those statements made prior to being read your Miranda Rights, your case may be dismissed.  However, usually a prosecutor will have other evidence to be used against you in court.