... what happens when someone is totally deaf? One of two things. Either, they learn a signed or spoken language and from then on use that language to talk to themselves, dream, and all the things you do with yours. Or, they never learn any language in which case they think, dream, and talk to themselves without language.
Contrary to popular wisdom, adults without language not only exist, they aren't that hard to find. They hold jobs, they tell stories, they do math. Susan Schaller's book describes what it's like: if you are interested in linguistics you should have already read it and if you haven't, go read it now. Nieminen's book describes another languageless individual, this one making a living as a newsboy.
Schaller, Susan. 1991. A Man Without Words. University of California Press.
Nieminen, Raija. 1990 Voyage To The Island. Washington, DC: Gallaudet Univ. Press.