Either 3 or 4 would work.

It is a passive construction, so only 3 and 4 work. In spoken American/Canadian English, both 3 and 4 are natural. In written English, I prefer 4. For some readable general information about participle clauses, including passive past participle clauses (having been ...), here is a link: https://learnenglish.britishcouncil.org/intermediate-grammar/participle-clauses

I agree with Su.Ki. and Simon. 3 and 4 are both correct. To my ears, #3 sounds a little more casual.

I'd go with Su Ki or Simon. As between 3 & 4, I'd favor 4.

I'm going to contradict the other two people and say only 3, based on the position in the sentence. The past-perfect form ("having been") is used to show that one thing happened before something else. To use 4, I believe the sentence should be something like: Having been up in a small, dark cupboard for hours last year, she still has nightmares. You could also combine 4 and 3 to get the sentence: Having been up in a small, dark cupboard for hours last year, she still has nightmares about being locked in one.