。
Nobody knew that I, too, had an impossible dream.
Literal
I [to-に-も] unattainable dream [subject-が] exist-was [quotative-なんて] no-one not-know.
かなわぬ is the classical/literary ぬ negative form of かなう ('to come true, to be realized') — 'not come true, unfulfillable.' The ぬ ending is an archaic alternative to ない, still used in set phrases and poetic language. なんて is a casual version of などと, here marking the quoted thought with emotional emphasis — 'such a thing as.' The whole sentence has a wistful, dramatic quality.