Life is trickier with files that were not in your iTunes fodler.
The iTunes library database stores the full path to music files and cannot accommodate any change to this if the file was not in the iTunes media folder.
If you your new PC has the same OS and exactly the same folder structure right down to the account name, you may be able to get away with copying the folder into the equivalent location on the new PC.
If, for example the path to a track on the old PC was
c:\users\youraccount\music\myothermusic\artist\trackname.mp3
It would have to be exactly the same on the new PC.
If this is not the case it may be possible to edit iTunes Library.xml to correct the path, and then recreate the iTunes library from the xml file, but you would not end up with exactly the same iTunes as all the date added fields would be the current date.
Normally when move an iTunes library to a new PC you would consolidate the library first to avoid the issue, but I don't see this working with an external drive as you face the same issue there.
It is easier to just add the tracks to your library and sacrifice the playlists unless the number of tracks is so small that you can find each track individually in iTunes.
(when adding tracks from another drive, you need to have copy to iTunes media folder when adding to library checked in preferences in order to ensure the tracks are copied.)