If you device is still working (and touch screen is broken), you can connect a mouse to your phone's microUSB port (get a USB mouse, and connect it to a USB to microUSB connector).
Now, you can transfer your files to cloud storage (google drive, dropbox, box etc), and access it from your PC.
For future, setup auto-backup of your photos to Google Photos (using the Google Photos app). Your contacts/calendar data should be getting auto-backed up to your Gmail account (assuming you didn't disable sync). Any other data that you need, you should set up an auto-backup for that as well (describe what you need backed up, and maybe we can help)