A320 Captain reported a stuck Press To Talk button hampered communications; requiring a divert and precautionary landing.

Narrative

Preflight and departure were normal. In cruise at FL370; we received the 'COM Single PTT(Press To Talk) Stuck' ECAM. This was accompanied by 'HF 1 Transmitting' and 'VHF 1 Transmitting' in orange. We completed and cleared the 'COM Single PTT Stuck' ECAM a few times; but it would return again within a minute; so we eventually left it displayed. The 'HF 1 Transmitting' and 'VHF 1 Transmitting' messages came and went randomly for most of the rest of the flight. FO (First Officer) was PF (Pilot Flying) this leg and he remained so through the eventual landing.Additional indications:Unable to transmit or receive via any means. VHF; HF; SATCOM; INT; and CABIN on all ACPs (Audio Control Panels) were all completely inoperative. (No radio transmissions received on any radio for the rest of the flight.)The SATCOM screen on the MCDU (Multi-Function Control and Display Unit) flickered; and it switched rapidly back and forth between 'ready' and 'dialing.'There was loud pulsing static in both cockpit speakers; and in the overhead speakers throughout the cabin. (Learned this later in event from flight attendants.)We put on our headsets; but same loud pulsing static was present. Unable to communicate via Interphone (INT). Headphones not used for the rest of the flight.Random orange 'call' light and buzzer from the cabin every 30 seconds for first few minutes of the event; then it stopped. Later determined to be spurious - cabin was not calling during that time.We tried to call the cabin but the 'CABIN' ACP function was inoperative. EMER Cabin Call tried but also inoperative.We sent an initial ACARS message to Dispatch that we had lost all comms. We set the squawk to 7600.We ensured all green TX buttons were deselected on all three ACPs. We used the overhead ACP switching panel to see if we could gain comms via ACP 3 on either the Captain or FO side of the airplane. No change to the above list of indications. In fact; when we tried to engage any green TX button on any ACP; it would extinguish by itself after 2-3 seconds. If any ACP listening button was raised (white) we heard either the pulsing static or nothing. Observer hand mic and headset tried - no change. These were then unplugged. Both RMPs (Radio Management Panels) were switched off for a minute; and then back on. No changes.At this point we were out of ideas and outside the QRH; so I made a WiFi call on my personal phone to Dispatch. My airborne WiFi phone call was made via a wireless ear bud in my left ear only; so I could hear the FO with my right ear and keep both hands free to fully attend to my duties as PM (Pilot Monitoring).I explained our situation via phone call to Dispatch and they immediately conferenced in Maintenance. We spent at least 15-20 minutes on the phone with Maintenance trying to find any reset or other action that would restore comms. The only viable airborne reset found was for FWC (Flight Warning Computer) 1 and FWC 2. Maintenance directed us to try those resets; but there was no change; except to also knock ACARS offline for the rest of the flight. ATC was conferenced into the phone call; and they provided holding instructions over ZZZ at FL370.We were only able to communicate with the flight attendants by passing notes on paper back and forth under the cockpit door. We wrote to them to knock if they had an urgent need. I tried the cockpit PA handset and miraculously it did work. PA's were able to 'break through' the static on the cabin speakers; so I was able to make PA's to the cabin to keep the flight attendants and customers informed of the situation.In coordination with Dispatch and Operations Control; the decision was made to divert to ZZZ1. Dispatch requested priority handling for the flight and we concurred. Dispatch conferenced ATC in on my phone call again; and clearance to ZZZ1 was provided via the phone call. As we began the divert towards ZZZ1; the F1 knocked on the door. I looked through the peep hole and saw two flightattendants but no cart. We had only 42 passengers on board and I saw all were seated. Based on our agreement that a knock meant an urgent need; and the fact we had begun the divert and time was limited; I exercised my Captain's authority and opened the cockpit door to let the F1 into the cockpit. She communicated that the customers had 'seen our flight turn red on FlightAware/FlightRadar24' and were growing concerned. I was able to show her what we were dealing with in the cockpit. I also told her we had just turned towards ZZZ1 and would land in approximately 25 minutes. She understood the situation and the plan; and she returned to the cabin.Via PA; I advised the Customers of the divert to ZZZ1 and that we expected a normal landing and taxi to the gate. Further clearance for the approach and landing were passed to us from ATC via the WiFi phone call. At top of descent I asked for a follow-me truck to guide us on the ground to the gate. Landing and taxi in to the gate were normal. Follow-me truck was waiting for taxi in as requested. Logbook write-up made. Thorough verbal debrief completed with ZZZ1 Maintenance personnel.