Reinstalling Windows 10 on Surface Pro 3

Use the official recovery image and the following process. Go to
https://support.microsoft.com/en-us/surfacerecoveryimage   (with a different Windows computer if yours is not working properly)  and download a recovery image for your Surface. You will need a 16GB or 32GB USB
stick formatted FAT32 (use a Windows computer).  Best to purchase and use a new,
previously unused USB stick for this. Use FULL format and not quick format and
give the volume a name like surfboot. Unzip/extract the recovery zip to the root
of the formatted USB stick and then-

To reset your Surface from a USB recovery drive:
Step 1:    Make sure your Surface is turned off and plugged in (hold down the power
button for 30 seconds).
Step 2:     Insert the USB recovery drive into the USB port on your Surface.
Step 3:    Press and hold the volume-down button while you press and release the
power button on your Surface.
Step 4:     When the Surface logo appears, release the volume button.
Step 5:    When prompted, select the language and keyboard layout you want.
Step 6:     Select Troubleshoot > Reset your PC.
If prompted for a recovery key, select Skip this drive at the bottom of the
screen.
Step 7:     Select the target operating system you wish to reset. This
refers to the current operating system installed on your Surface.
Step 8:    Select Yes, repartition the drives, and on the next page, select Next.
Step 9:     Choose Just remove my files.
Step 10:    Select Reset.
Surface restarts and the Surface logo displays while the reset process continues
(this can take a while).

Whyyyyy

If you received this message using the downloadable recovery image, I would like
you to try the Surface Data Eraser - documentation at
https://docs.microsoft.com/en-us/surface/microsoft-surface-data-eraser  -  the
download itself is at
https://www.microsoft.com/en-us/download/details.aspx?id=46703   -- if this tool
reports an issue, please take a picture of it and post it. If it runs
successfully, try the recovery USB again.

My result. When I went to reset my PC with the recovery image I got the same error.. :(

You provided an image of the output of the SDE, but not what happens when you
use the recovery image.  Be sure to see step 6.

Go to https://support.microsoft.com/en-us/surfacerecoveryimage   (with a different Windows computer if yours is not working properly)  and download a recovery image for your Surface. You will need a 16GB or 32GB USB
stick formatted FAT32 (use a Windows computer).  Best to purchase and use a new,
previously unused USB stick for this. Use FULL format and not quick format and
give the volume a name like surfboot. Unzip/extract the recovery zip to the root
of the formatted USB stick and then-

To reset your Surface from a USB recovery drive:
Step 1:    Make sure your Surface is turned off and plugged in (hold down the power
button for 30 seconds).
Step 2:     Insert the USB recovery drive into the USB port on your Surface.
Step 3:    Press and hold the volume-down button while you press and release the
power button on your Surface.
Step 4:     When the Surface logo appears, release the volume button.
Step 5:    When prompted, select the language and keyboard layout you want.
Step 6:     Select Troubleshoot > Reset your PC.
If prompted for a recovery key, select Skip this drive at the bottom of the
screen.
Step 7:     Select the target operating system you wish to reset. This
refers to the current operating system installed on your Surface.
Step 8:    Select Yes, repartition the drives, and on the next page, select Next.
Step 9:     Choose Just remove my files.
Step 10:    Select Reset.
Surface restarts and the Surface logo displays while the reset process continues
(this can take a while).

I have seen this before. When you get to step 6 look for a button that says install form another drive and try that, then follow the rest of the steps.