being born deaf is not "normal" in the sense that being born with MS or autism is not normal. but then one must define "normal". i would call it the phenotype that best adapts an organism to its environment. in almost every species but homo sapiens, natural selection prevents disadvantageous traits from persisting through more than a generation or two. a deaf tiger in the wild would probably not live to reach sexual maturity and make more deaf tigers.
with humans, natural selection doesn't really apply. a child could be born blind, deaf, autistic, retarded, with no legs and 5 arms growing out of its chin and as long as none of these things were fatal to the infant and it lived long enough to reproduce, those genes could potentially be around forever. hearing is not essential for human survival, and as long as deafies continue to pair up and have deaf children, deafness will persist for as long as it can before medical technology erases all potentially harmful genes from the human race.
for now, "normal" is mostly a question of numbers. the vast majority of the population is healthy. so by default, anyone that is deaf or has webbed feet or purple skin is not normal, because he or she is in such a small minority group. however, if in 3 million years, hearing was no longer necessary and 98% of people are deaf, you'd find that deafies are the new "normal" and hearies are the "disabled".
incest is clearly not the only cause of deafness. anyone who says "s/he's deaf because his/her mom and dad were siblings" should be shot.