Probably I mentioned somewhere in this forum, the etymologies of the particle で and copula だ/で are the same, so the definition is not always clear. The function/meaning of で is determined by the relation of the two clauses/phrases/words preceding and following で. As for your example, both interpretations, particle and copula, are possible. Anyway, 大成功 is the cause of 長期興行 in either cases.
それは、大成功で長期興行になった。(particle) vs それは大成功で、長期興行になった。(copula)
(The latter seems natural to me.)