Recently while giving a lesson in a newer warrior with dual GNS430s, comm 1 decided to no longer transmit after liftoff. My student and I were remaining in the pattern and getting calls in the crosswind which were unanswered by the tower it seemed. My student was on the radio as I'm trying to get him ready to solo. He got distracted by the failed radio, and was in a 1000fpm climb out of the pattern, passing through the downwind. I tried at the same time to answer tower on my radio, while telling my student to descend and turn downwind, immediately. I should mention this was superbowl weekend, so there were a steady stream of business jets departing for Indiana...oh and did I mention there were about 5 other students in the pattern!? So, needless to say it was a busy time, and the expected New England winter bumps weren't helping my student's concentration. I took the controls, and continued to try to communicate with the tower. At this point, I should have tried comm 2, but ATC started to call my traffic and clear me for a touch and go! Without hearing me? This seemed odd, and I later learned that the controller was a trainee. He sequenced me in for landing, I had my traffic, so I did what I thought was best, and squawked 7600, telling my student to watch the tower for light gun signals. We never saw them, so I landed, and taxied off the runway. I changed to comm 2 and they heard us, so we continued the lesson on that radio. On the way back from the practice area, I tried comm 1 again and they heard us, so I just squawked it at the FBO as intermittently working.
The takeaway I tried to teach my student was the seminal aviate, navigate, communicate. In hindsight switching to comm 2 to troubleshoot in the downwind would have been the better idea but I was trying to descend and join the downwind with others in the pattern while the tower was still making calls to me. Instead I aviated and navigated to get back in the downwind. Since I was unable to answer back my clearance right away while concentrating on seeing and avoiding, the first thing I thought was squawk 7600, i.e., take the failure out of the mental conveyor belt that is flying...and lo and behold; that counts as communicate!
...But I never got to see any light gun signals... :(