In Florida, as in most states, driving is not actually an element of DUI. The relevant question is; were you in actual physical control of an operable vehicle? Actual physical control can mean sitting in the front seat with the motor turned off and the keys in your lap. In your case, it sounds like you're going to want to argue that while you may have been in actual physical control, your vehicle was inoperable because it overheated. If you drink and render your vehicle inoperable by driving drunk into a wall, then you cannot claim that the vehicle was inoperable to avoid a DUI. However, if your drinking did not take place until after the vehicle became inoperable, then the inoperability had nothing to do with the alcohol, and there was no chance for the alcohol to mix with driving because you couldn't drive. You need to hire an attorney to file a motion to dismiss based upon the inoperability of your vehicle.
This response does not create an attorney/client relationship. You need to hire a lawyer in your area that handles a lot of D.W.I. cases. D.W.I. is one of the most complicated misdemeanors in our State. Based on what you have posted, you have an excellent defense to these charges and this case needs to be tried. In North Carolina the burden is on the State to prove beyond a reasonable doubt that you operated that vehicle while subject to an impairing substance while being .08 BAC or above or appreciably impaired. See a lawyer soon. Good luck.