Let us try again...
Here are typical layouts for the iTunes folders:
In iTunes under Edit > Preferences > Advanced there is an option to choose the media folder. Changing the media folder changes the path to the section outlined in red. The library files stay where they always were. When you say you were operating iTunes from the external drive, or my library is in F:\iTunes you either mean that F:\iTunes is in the layout as above (1), or that F:\iTunes corresponds to the iTunes Media folder in the above diagram (2).
In the first instance (1) moving the library to a new computer is simply a matter of connecting the drive, then shift-starting iTunes to open the library file at X:\iTunes\ITunes Library.itl where X: is the drive letter.
In the second instance (2) you only have the media. As I understand it you want to build a portable library on the external drive. This set of steps will work for your current situation:
- Rename F:\iTunes as F:\iTunes Media
- Delete any library files and/or Album Artwork folders that are in F:\iTunes Media
- Shift-start-iTunes and create a new library at F:\iTunes
- Move the iTunes Media folder inside F:\iTunes, merging with the empty folder there
- Use File > Add Folder to Library to add the folder F:\iTunes\iTunes Media
tt2