PakChenny

Alternative solutions: 1. Insert an SD card to your note 3 and back up pictures (and/or other files) to SD card, and then move the pictures to elsewhere. 2. If you can install apps on your phone, then choose a reliable backup app which can store backups to cloud. 3. Install Side Sync both on your PC and phone(via Play Store or APK file in SD card), and try to connect the two device with Side Sync via WiFi. Then back up pictures to PC. http://www.samsung.com/us/sidesync/ 4. Repair the charge port.

Don't have an Xperia Z3. Android devices have different ways to enter recovery mode, though usually involve some combination keys. Moreover, some third party tools can boot most phones into recovery mode easily. You can check a tutorial here.