HELP! My screen went to snow!!! Need to get to my memory, not backed up!

[AC Question]

My screen all of a sudden is blinking on and off and is sort of a grey/light blue snowy color. I have received a replacement phone, but have some very important audio files on an app called Smart Voice Recorder on my old phone that I need to get to. I am not too smart, because I didn't send the files via e-mail or Drop Box as the app recommends. As far as I can figure out, it doesn't have an automatic cloud back up within the app. Right now, they are just on my phone, that I can't look at because of the snow. Does anyone know of a way to get to these files before I have to send the old phone back? Is there a way to back it up to a computer if I can't see the screen? If so, what type of cord do I need? Thanks for any help I can get!