Captain reported communications problems caused the aircraft to begin rolling after the tow bar and tug were disconnected prior to parking brake being set. The Captain used normal brakes to safely stop the aircraft and used visual signals to reestablish communications.

Narrative

Just before pushback in ZZZ; the Ground Crew had to find a replacement headset because their original headsets did not work. Once they found a new headset pair; they made positive communication contact with the flight deck. The First Officer contacted ground for the pushback clearance. Once cleared for pushback I called Flight Deck to ground and stated; Parking brakes released; cleared to push. The Ground Crew commenced the push back. Moments later the Tug Driver stated Cleared to start. I repeated back; Cleared to start. I asked the First Officer to start both engines since we were going to be number 1 for takeoff. The airplane was pushed back into an area near the taxiway. The push back came to a stop and then we heard no communications. I called Ground numerous times but no answer. The Marshaller which gives the all clear signal after push back was standing about 50 ft. away; no exaggeration; in the dark with the wands crossed. There was someone on a tug next to the Marshaller flashing the headlights of the tug our way. I was unclear as to what that meant. I then opened the window and signaled for someone to come closer to the plane so I called clearly see what was going on. Was it hand signals or were they trying to tell me something. I continuously signaled to them that I could not hear anything on the headsets. The next thing that happened was the tow bar being connected and the airplane starting to roll. I quickly stepped on the brakes and set the Parking brake. I then took my headsets off yelled out of the window do not disconnect; the brakes were not set. Nobody could hear because by this time the number 1 engine was running.I quickly contacted operations on the radio and explained what just happened and that someone could have been seriously hurt or aircraft damage. I have two of the rampers literally standing in the dark and I cannot get any signals from them and the headsets cut out again after finding a new headset. Operations assured me they would have a conversation with the crew.