Ah, yes. Lollipop changed things in regards to MTP connections. It used to be that you could just plug your device into a computer and browse your internal storage. Now you need access to the display when you plug in your device and you have to pull down the notification shade to switch from charge only to mtp.
are you using Google Photos to back your photos up? If so, you should be able to access them either online or on another device. If not, there aren't really a lot of options short of a screen repair, unless you already have USB debugging enabled on the device and/or an unlocked bootloader.