Air carrier Captain reported a miscommunication with Dispatch regarding the flight crew's final DG summary and acknowledgement message during pushback. The final DG summary and flight crew's acknowledgment messages were rectified prior to aircraft taxi.

Narrative

During preflight preparations; parked at gate X; we received a Planned DG (Dangerous Goods) summary over the ACARS printer. After closing the aircraft doors and getting ready to push I didn't realize we had never received a final DG summary. Upon pushback I received an ACARS message to respond with an acknowledgement for dangerous goods accepted. I glanced at the ACARS printer and saw a piece of paper there and assumed it was the final DG summary so I responded in ACARS with the acknowledgment meaning dangerous goods accepted. I then looked at the paper in the ACARS and realized it wasn't the final dangerous goods document. This occurred all during the pushback from gate X. I then contacted operations and asked if we did in fact have dangerous goods loaded on board. After checking with the ramp; operations advised we did in fact have dangerous goods on board and they would send the final DG summary. After waiting a couple of minutes I still had not received the final dangerous goods summary over ACARS. At that moment operations called me back and stated they resent it to us via ACARS but in case we didn't get it he also emailed it to me. I checked and in fact had received it in my email but still not over the ACARS. I responded again in the ACARS with another message to acknowledge that I had in fact received the final DG summary. We then continued with the flight. It should be noted that when I became aware of this issue we did not taxi any further. We stayed on the ramp and dealt with the issue before taxiing under our own power. It should also be noted that while parked at gate X we kept getting ACARS NO COMM messages on our FMC.