I'm unable to start up the game as it says CD key invalid. anyone have a solution?

Next to Launch there is MORE in Galaxy client. Somewhere there game verification. If you use Galaxy and Galaxy versions.

For GOG offline version reinstall it to path like X/Games/Empires-DotMW/ (not C/ drive) as admin and do first start as admin (grom setup finish screen are good since setup is in admin mode game started from it also get admin mode).
Some games require admin mode all the time - if they require HKLM Registry section for basic config (instllpath or CD-keys)(ingame settings go to VirtualStote by Windows security and that OK).

For Galaxy (or Steam /etc) it should be like X/Games/Steam/ and X/Games/SteamApps/ for games. All not on C/. Reinstall as admin. Make launched and configure client in both non/admin modes. Restart Galaxy as admin to install or verify game. Make verification after every downloadings in any clients have that feature.
So verify Empires DMW at least twice in admin mode. Current Galaxy no more report verify result. You must do it twice then. Start game from Galaxy that is still in admin.

After that you can restart Galaxy normally no-admin and start game from it in no-admin.

Sometimes this Wiki provide useful info
[url=http://www.pcgamingwiki.com/wiki/Empires:_Dawn_of_the_Modern_World]http://www.pcgamingwiki.com/wiki/Empires:_Dawn_of_the_Modern_World[/url] (more links there incl GOG Support)

you just need to find another cd key and type it in.

where do you insert the new CD key?

you do it when the game starts up.