"Да нет" is a common way to say "no" when outright "нет" seems like too strong of a word, or when there's some level of uncertainty. You'll hear it daily, and as for translation it can be translated as "I guess, not", "rather not" or something along the lines.
"Да нет, наверное" was made into a catch-phrase by a popular comic Zadornov (if I'm not mistaken), who used it to demonstrate a 'complexity' of Russian language, in which three contradicting words form a meaningful sentence. It means simply "Probably, not".

PS. Just to make it clear - "да нет" NEVER means "yes".