Option number one. If you have a google account, your photos may have also been saved there as well as your phone. From a computer, try logging into your google account and see if they are in the "Photos" area.
Option number two. You will have to try hooking it up to a computer and see if the computer can detect it. If it can, great! Then you can move your photos and info over to the computer, and then onto a new phone when you are ready. If it doesn't detect the phone, then that won't work.
Option number three. If your photos, etc., were saved to the phones SD card rather than the phone itself, you can try placing the card into another phone (or your computer if you have that ability) and get the files from there.