will not let me sign in to imessage

ive tried a hundred times... customer support failed us as well... i have full wifi, everything else works, safari,email,etc. but as soon as i go to setttings & either imess or facetime, same respoce... "could not sign in. please check your network connectin & try again." my network is fine! i swear ive been trying to fix this since christmas... for my daughter.

i tried reseting factory setings& all the above.

anything else???