Another sentence that sounds unnatural

AnonymousIs this sentence correct?

Strictly, yes; practically, no.

Since it was a holiday, the train was full.

many thanks for the swift response. But I learnt that participle phrase is only used to refer to the same subject in the sentence. For example: walking down the road, I met a nice lady.

AnonymousI learnt that participle phrase is only used to refer to the same subject in the sentence.

Only when the participle has no subject of its own, but in your original sentence, it does.

Does that mean I can also say: "Sara being my girlfriend, I was happy"?
"Sara" here and "it" in the original sentence play the same function.

Is this sentence also correct?

AnonymousDoes that mean I can also say: "Sara being my girlfriend, I was happy"?

Yes indeed, but again natives do not use that structure; we generally eschew 'being' clauses.

I was happy because Sara was my girlfriend.