Under the ordinary diptote rule, nominative takes ḍammah, while accusative and genitive take fatḥah, without tanwīn.
The second element of Baalbek therefore appears as:
Nominative — بَعْلَبَكُّ
Accusative — بَعْلَبَكَّ
Genitive — بَعْلَبَكَّ
The first element بَعْلَ remains fixed on fatḥ. The added vowels are pedagogical; the source prints the three example clauses unvowelled.