As I understand it you don't have anything other than the media that you mind losing, and you'd like your library to be on your external drive.
I'm assuming there isn't a folder called G:\iTunes - If there is rename it to G:\iTunes OLD before you start.
With iTunes closed, press and hold down shift as you click the icon to launch iTunes. Keep holding until asked to choose or create a library. Click create. Browse to G:\ and create a library called iTunes. This will create and open a new empty library for you at G:\iTunes whose media folder should be G:\iTunes\iTunes Media. Use Edit > Preferences > Advanced to double-check and correct if needed.
Using Windows Explorer move the media that is currently stored on drive G: into G:\iTunes\iTunes Media then in iTunes use File > Add Folder to Library to add the folder G:\iTunes\iTunes Media.to the library.
You now have a self-contained portable library in G:\iTunes. 🙂
You can delete all of the content at C:\Users\<User>\iTunes to recover space on your internal drive.
You really should backup G:iTunes to another external drive at the earliest opportunity. See the user tip Backup your iTunes for Windows library with SyncToy for a backup strategy. Copying by hand is error prone and time consuming.
If you want to use the library on a different computer, or the drive letter changes for some reason, you can shift-start-iTunes and choose the library file at X:\iTunes\iTunes Library.itl where X: is the drive letter currently assigned to the drive.
tt2