My ps4 only displays on 1 out of three TVs

My PlayStation only works on one out of the three TVs we have. So basically we bought a new smart tv that we have in our living room. I decided to take my PlayStation to the new tv to see how it was. After trying the new tv out I went to put my ps4 back in the tv it wa in before and it didn't work. So then I put it in the other tv we have and it still didn't work. I updated my ps4 and the two TVs it didn't work on and still nothing. Changing the hdmi cable The resolution of the ps4 done nothing either , I called Sony and they said this was very strange and that they didn't know what to do. And now I can't use the PlayStation that had hundreds of pounds worth of games and dlc on which is really bad. If you could help with this problem I would be very happy