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So I'm posting this for anyone else who may have uninstalled/reinstalled during the outage that now finds themselves with an empty library in Galaxy after getting an error that their library couldn't be recovered such that it tells you to try to scan for it. (Sorry, I don't have the exact message.)

My operating system is Windows 10 (64-bit).

1) Uninstall GOG Galaxy... again.

2) Go to C:\Program Files (x86)\GOG Galaxy
Delete everything except for the Games folder

3) Open the Windows ribbon, go to view, and put a check next to Hidden Items. (You may need to expand the window.)
Go to C:\Users\whatever_your_username_is\AppData\Local
Delete the folder
Backup to the AppData folder and go into the Roaming folder
If you see a folder, delete this also (I currently do not have this, but I'm pretty sure I deleted here also.)

You can uncheck the Hidden Items (if you want) and close the Windows ribbon.

4) Right-click on the windows button and select Run (or hit Windows Key + R) to open the Run box.
Type in %programdata%\
Delete the folder

5) Reinstall GOG Galaxy.

After you login, there will be a box at the bottom of the screen with an x off to the right side. This is telling you what percentage it is at importing your purchases from GOG's server. The only thing you need to do here is wait for this to be finished.

6) Click on the gear at the upper-left, select scan for GOG Games so that it can find the games you have already installed. The default patch is C:\Program Files (x86)\GOG Galaxy\Games

At this point, GOG Galaxy found the five games I had installed. However the game I was played and had crash on me at the time GOG Galaxy went down had an update available. The game really has no update as far as I could tell and was just repairing its installation. If you have this happen where an update is available for something with no update, I'd just let it do it's thing.