In any event, lots of things can go wrong before the tweeter. If you wanted to thoroughly diagnose it, get a Dayton audio DATS V2 to measure the impedance of your whole speaker a swell as the drivers out of the box.
One step below that is to remove the tweets and test with an Ohm meter. See if you have a short (no Ohms) or open (overloaded or infinite Ohms) circuit.