Welcome to the wonderful world of English homophones. The answer to your question is "rent" or (less often) "rended," but your example is problematic because the English word "rent" is used in many more common ways.
"The rent barn" will not be understood by most English speakers in the way you intend, because a) rend is an uncommon verb and its past participle is more uncommon still, b) the word "rent" is often used as a the first word in compound nouns like "rent check" (or cheque) or "rent control," and c) the word rent is most often used as a verb, as in "to rent a barn."
To my ear, "the rent barn" is the barn that you put out for rent.
Perhaps this is the reason that "rended" is listed in most dictionaries as a secondary option for the past tense. It still has a little bit of an archaic or poetic flavor to it.
Rended barn and scattered straw upon the field lay.