HP Simple Save 2 TB External Hard Drive (3.5-inch, USB 2.0) Broken HELP!

I've had my HP Simple Save 2 TB External Hard Drive for a few of years now, it's served me great, I used it for storing all my photos but the usb connector has snapped off from the small CD drive inside the casing.
This has simply been through use, it was working fine, not wobbly or mistreated in any way, it must have just came to the end of it's life and now I can't hook it up to my computer to get the photos, I'm desperate to get them back, wedding photos, birthdays etc most of you must know how I'm feeling.
So I looked up a few solutions, one was to buy a USB-to-IDE/SATA adapter and use that to connect to the computer, well it works as far as recognising that a device is connected but won't load the files or folders to view.

As I've looked around apparently the small CD drive that's inside the case has software that my computer automatically loads? Now this is where I'm lost, how do I manage to get this to work?
I'm almost at my wits end, as far as looking every single day on Amazon and eBay to buy a new one to transfer the CD drive onto the broken one to load it up and get my photos back, IF that would even work, I'm not sure.

So if you have any suggestions/help please please get in touch, thanks.