Broken LCD won't allow me to transfer data onto new phone (also S4)

[kte3]

The LCD is unresponsive, so when I tried removing the data via USB and my Mac, I learned that I had to switch modes on the phone from 'Media Device' to 'Camera PTP'...which I can't do. Is there anything that can be done to save my precious data (namely my 700 photos)? I don't have them on an SD nor are they on Backup Plus (to my disappointed surprise):

 

[srkmagnus]

The LCD is unresponsive, so when I tried removing the data via USB and my Mac, I learned that I had to switch modes on the phone from 'Media Device' to 'Camera PTP'...which I can't do. Is there anything that can be done to save my precious data (namely my 700 photos)? I don't have them on an SD nor are they on Backup Plus (to my disappointed surprise):

If you can't accept any prompts on the device, no. Every solution I can think of requires some form of prompt to be accepted on the device to either connect a service or the device to a computer.