If the police decide because of their investigation to arrest you for a specific criminal charge, they are supposed to read your rights at that point if they intend to question you any further.
If at the point you are under arrest they do not read you your rights, then anything they ask you after that point cannot be used against you if it goes to trial.
Your case being dismissed altogether depends on whether or not they can go forward on the evidence they have without those statements. If they do have enough evidence, then you probably won’t get your case dismissed just because they didn’t read you your rights. However if the evidence that they are relying on are the statements you made after you were arrested then you probably can get your case dismissed since they will not be able to use that evidence.