So, I followed all these different forum Topics but I'm at a loss.
I've found my Serial Key, there's no CDKey Changer or nwncdkey.ini or anything like that in either my documents or GOG folder :(

I've tried to input my Multiplayer Serial Key but for some reason it says "Invalid CD Key Entry"

Can someone please help? :(

Try to launch the game for the first time - the cd key should then be created.

Look for cdkey.ini instead. It's a basic text file, no need for CDKey Changer; just copy and paste your key in, save and restart the game. Also, I believe you must have a unique key, even to play on a LAN.

In case you mess up the file or wonder about the formatting, it looks like this:

;This is your CD Key for Neverwinter Nights.
;DO NOT share this CD Key with ANYONE.
;Apart from this installation, Beamdog, BioWare, and Atari will never ask you for this CD Key.
[NWN1]
YourKey=XXXXX-XXXXX-XXXXX-XXXXX-XXXXX-XXXXX-XXXXX

I checked my files both in my GOG directory and my Documents but the file doesn't exist :(

If you launched the game and the file doesn't exist, then it's either an Antivirus program or UAC preventing changes to Documents - Neverwinter Nights.

If you're like me and were searching in vain for this, don't look in the GOG Galaxy app.

Go to GOG in your web browser, <username>, Games, NWN:EE, More, Serial Keys and it should pop up.