Do you happen to know which version of OS X is currently installed on this Mac?
Shutdown your Mac.
Restart and, as soon as you hear the startup chime, press and hold the “OPTION” (or “Alt”) key at boot until a boot menu appears listing the bootable volumes in your Mac. This usually happens within 30 seconds.
Can you tell me what it lists?
Try holding down Option was soon as you restart, but before the grey screen appears then continue as instructed.
Then, select the “Recovery HD" volume.
Wait for “OS X Utilities” menu to appear (DO NOT CHOOSE TO INSTALL)
Choose Disk Utility from the available options.
In Disk Utility, select your normal, bootable hard drive volume from the list in the sidebar (usually "Macintosh HD").
Then, Click "Repair Disk" (or First Aid)
If it finds errors, repeat the process until it reports the drive is OK.
Next, click "Repair Disk Permissions" if available.
Once the process has completed, choose “Disk Utility” > “Quit Disk Utility” in the menu bar at the top of the display.
Then, restart your Mac and it should hopefully boot back into your normal Desktop.
you can see if you can manage to boot into Safe Boot mode and back up the photos.
Restart your Mac
As soon as you hear the Startup chime, press and hold the SHIFT key
Continue to hold the Shift key until you see the Apple logo and progress indicator.
Then, let go of the Shift key and let it boot to the Desktop (it may take longer than usual so please be patient).
Give it 10 mins max to boot to the desktop.
Let me know the results.
When you booted to the Recovery volume and ran Disk Utility, did you see the Repair Disk option or First Aid?