How do I extract files when the digitizer on my Samsung Galaxy S4 is broken?

[AC Question]

The digitizer on my Samsung Galaxy S4 is shattered, so I cannot do anything with the phone. I have very important things on my phone like memories of family etc but I don't know how I can get the files off it. I've tried plugging it in via USB into my laptop, but the phone will connect then disconnect. I don't know what I can do to get the files off the phone.