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Когда-то (the hyphen is needed here) means "sometime in the past" when one doesn't remember when exactly, so the sentence may be translated as "Once I lived in a thick tropical forest"

старый refers to an old year here (before meeting the New Year there's a tradition to see the old one off). A possible translation of the sentence is: I wish we had time to see the old year off.

Another example:
-Где Петя?
-Как ты не знаешь? Он же уехал на юг.
-Надо же! А мне никто даже и не сказал.
Note that it's wrong to use никогда with a perfective form of a verb, it requires the...