If the overt noun is a subject, it is nominative; if an object, it is accusative.
In «ضَرَبْتُ وَأَكْرَمَنِي زَيْدٌ», governing by the second verb makes «زَيْدٌ» nominative, while the first verb’s object is understood but omitted.
A proper analysis identifies the governor, grammatical role, case ending, and any omitted argument or pronoun.