First of all, you can use a web browser to log into gog.com and
download the offline installers from your library. The only game that requires GOG Galaxy is Gwent: The Witcher Card Game, which is online-only multiplayer.
Secondly,
open a support ticket if you haven't already. Zip up the
C:\ProgramData\GOG.com\Galaxy\logs folder and attach it to your ticket to speed things along. Getting a response from support can take quite a while, but they do get back to you eventually.
While you wait for a reply, you can try the following:
1. Uninstall GOG Galaxy from Control Panel/Settings app.
2. Manually delete the following folders afterwards, if they still exist. Only do this if you never managed to start it up, so you don't have any custom settings saved. If you don't have hidden files and folders displayed, you can paste the path into the File Explorer address bar, go up one folder, then delete the target folder.
C:\Program Files (x86)\GOG Galaxy C:\ProgramData\GOG.com\Galaxy %LocalAppData%\GOG.com\Galaxy 3. Install both
vc_redist.x86.exe and
vc_redist.x64.exe.
4. Restart your computer.
5. Install GOG Galaxy using
the latest full installer. The first link is for Mac and the second for Windows.
Edit: fixed typo.