You may not have the specular nodes set up quite right, or they need to be tweaked for this hair.

The purpose of the blend node between the blinn shader and the alternate_specular input on my example is to apply the transparency map to the blinn shader, Stewer is doing the same thing by plugging his Image_Map_3 into the Anisotropic shader's Specular_Value node.  You may certainly bypass it for a test render as SamTherapy says. 

Try setting the blinn node Specular_Color to white.  Also increase the SpecularRollOff and Eccentricity towards 1.