Linux may be able to mount the drive and let you copy your files. Download Tharpup here. tahr-6.0.2_PAE.iso You can burn the iso to disk on a Windows 10 by right clicking the iso and selecting Burn Disk Image.
If you are running Windows 10 on a OEM computer like Dell or HP you will need to disable SecureBoot and possibly Quickboot or Fastboot in UEFI. You may also need to enable Legacy Boot or it is sometimes called CSM boot. On Dell you can tap F12 at boot to bring up a boot menu for selecting your boot device. On Hp it is F9.
Once on the Puppy Desktop you will notice your hard drive partitions in the lower left labeled sda1...sda2...sda3.. and so on depending on how many partitions are on your internal drive. Attach the USB external drive and a USB icon will appear on the desktop. Click once on it and Puppy should automatically mount the disk and open a File Manager.If Puppy cannot mount the disk and open a File Manager proceed no further and post back.
Click once on your WIndow sdaX partition. I am not sure which one this will be as Windows 10 creates additional partitions. It may be sda3. The partition will mount and a File Manager will open showing the partition's files. If you do not recognize your Windows files and folders then close the File manager and try another sdaX partition until you find the correct one.
You can highlight the files in the USB external's File Manager by Ctrl+left clicking files/folders or by windowing around them while holding down your left click button. Drag your highlighted files from the USB File Manager window to your Internal sdaX window. A small dialog window will open. Select Copy and check the Quiet box. You will need at least the amount of free space on your internal drive as what you are trying to recover. Once you have copied over the files, exit Puppy and reboot. See if you can open your copied files. You may want to only copy a few first to see if they are corrupted or not.