IF the coolant in the radiator was frozen solid and you drove for ten minutes or so then it is possible the engine actually overheated and has seized up (particularly if it is petrol)- that's my worst diagnosis! Unfortunately I can't think of any other explanation. I am a little confused however because you say the engine wont turn over BUT you can hear the starter motor. If the engine has seized the starter motor will simply try and turn but fail to. If you can hear the starter spinning round then either the engine IS turning over or the starter is not engaging with the flwheel.
Hope it's not as bad as I am suggesting!
Richard
January 2009