Air carrier Captain reported an aircraft issue during taxi out that resulted in the aircraft not being useable for the flight.

Narrative

I did not sleep as well as I would have hoped in ZZZ1 due to the circadian swap from our afternoon departure out of ZZZ2 to and early morning departure on the east coast. In addition; the light from the hallway did penetrate the perimeter of the hotel room door contributing to my poor sleep. Upon arrival in ZZZ; we were alerted to an extended sit due to our next flight's delayed departure. After arriving at the aircraft; we received an updated EDCT (Estimated Departure Clearance Time) extending our delay. After initially boarding the aircraft; we were informed of a ground stop in ZZZ3 requiring all passengers to deplane. After much coordination we reboarded the aircraft. After closing the door; we received another significant delay and deplaned the aircraft once again. Approximately 4 hours after our original departure time we boarded once again and pushed off the gate. Taxiing out we experienced a maintenance issue requiring a gate return. We worked with maintenance at the gate until it became clear this aircraft would not be operating the flight. Once all passengers were deplaned and we were able to regroup we realized how tired we were. At that time we determined we would call fatigue.