What category airplane, Pub User, and what level TCAS?
Arinc spec for ACAS/TCAS II has the transponder relay altitude data to the TCAS, and there is no direct connection between the ADC and the TCAS interrogator.
TCAS doesn't interrogate mode A from the other aircraft's transponder, only mode C and mode S (if equipped). Aircraft B cannot see a plane without operative mode C.
Aircraft A TCAS will annunciate Fail if it is not receiving own aircraft altitude - and aircraft id number - from its transponder, which isn't clear in the question. Without a working transponder, moreover, there can be no aircraft to aircraft maneuver coordination.
GB