Blown tweeters

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.

How do you know they are blown, by the way? 

Often we don't even hear when a tweeter goes out.  A midrange though... :)

Contact the manufacturer.  The crossovers may have protection circuits.