One common misconception is if the police don’t read you your rights, then the case will be dismissed. This is not the law. Any statements that you made that were incriminating while in police custody (meaning you were not free to leave), if you were not read your Miranda Rights, must be suppressed by law. But it doesn’t mean that your case is automatically dismissed. For example, if you shot someone and you’re charged with battery with a deadly weapon, with substantial bodily harm and police take you into custody, if they don’t read you your Miranda Rights, and you say, “I shot Johnny,” (if it’s not suppressed) that would be incriminating. Based on that statement, you could be convicted.
In addition to your statement, if there is someone there who says, “Yes, I saw Mr. X shoot Johnny.” Even if they suppress your statements, you would be convicted. If there is additional evidence such as an eyewitness you can still be convicted, and your case won’t be thrown out.
However, if the only evidence they have is your statement and your statement is illegally obtained, because you weren’t given your Miranda Rights, then the prosecutor would not be able to proceed.