The Collaborative International Dictionary of English v.0.48:

deaf-muteness \deaf-muteness\, deaf-mutism \deaf-mutism\n.
   the condition of being a deaf-mute; a congenital deafness
   that results in inability to speak.
   [1913 Webster WordNet 1.5]

WordNet (r) 3.0 (2006):

deaf-muteness
    n 1: congenital deafness that results in inability to speak
         [syn: deaf-mutism, deaf-muteness]