Is there an iTunes Library.itl file on the external drive? If so shift-start-iTunes, click Choose, and browse to it.
If not can you retrieve it from the previous computer? If so see Make a split library portable.
If not shift-start-iTunes, click Create, make a new library at X:\iTunes where X: is the drive letter, move all of your media inside X:\iTunes\iTunes Media, use Ctrl+B if needed to enable the menu bar, then use File > Add Folder to Library to add the contents of X:\iTunes\iTunes Media to the library. If you have any devices see Recover your iTunes library from your iPod or iOS device to recover ratings, play counts, playlists and associate your devices with the new library without losing data.
See also Backup your iTunes for Windows library with SyncToy.
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