It probably won't help in this case but I run into that situation with some frequency on my clients desktops and laptops. I remove the drive & plug it into a USB blackbox attached to a working computer and unless the drive has gone bad, I can recover data off the non bootable drive. If this were a case of not working about the cost, you might be able to tear the Surface apart and remove the SSD and find a way of attaching it as a second drive on another computer. I would only recommend trying this kind of scenario, if your data is extremely important.
I'm not smart enough about the Surface to know whether you could attach an external USB drive that you can boot from and possibly see the boot-dead internal SSD drive.