It's not clear to me what your ultimate objective is. If you're trying to use the iTunes library on the external drive, start iTunes on the Mac, immediately hold down the option key and when it asks you to locate the library guide it to the iTunes folder on the external. This is assuming you keep everything related to iTunes in that one folder (library.itl, media files, artwork, etc.).
My ultimate objective is to store all media on an external plugged into my router so as to not waste a ton of space on my device.
I tried the step you mentioned previously, but it didn't work. Do I need to copy the .itl file and others from the original location on my computer's default itunes folder and paste it in the external for it to index/read it correctly?
On my lenovo, whenever I wanted to add music the library I just clicked add file/folder and it did it...
Am I missing something here? I thought itunes would be easier to use on a mac. (No bashing, just saying.... I'm still learning).
Perhaps you could outline what is stored on the external drive. iTunes isn't just a single file or set of media files, it is a whole series of files and folders that work together. Typically they are kept together. You can split them up to some extent but you have to know what you are doing.
What are the iTunes library files? - http://support.apple.com/kb/HT1660
More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management
What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html
It is starting to sound to me like you have the iTunes folder on the computer and the media files on the external. You can try copying the whole iTunes folder from the old computer to the new one and use the option key trick I noted above. Hopefully it can still find the external that way.
I get the impression the old computer may have been a Windows machine. I have no experience with working with drives attached to a router but I am concerned that you may have to reformat the drive to work with a Mac. This will require you wipe the drive completely so you will need temporary storage for files on there.
At this stage I suggest a time out for you give us background on your old computer setup and what it is you have stored on the router in terms of files used by iTunes.
I'll answer my own question here as it seems we're going off on a limb and I think this situation applies to many who just have a huge music colleciton and it's not an "itunes library" or formatted as such per se.
From my understanding there is a difference between an actual "itunes library" and what I keep which is a folder named music with subset folders for each artist, then album, then straight mp3/mp4/whatever files. I don't have an "itunes library"; I have a massive folder with media. All I had to do was uncheck the copy files option under the advanced tab in preferences. The I went to add to library under file and checked the folder I have in the external drive attached to my router.
This actually just (what I call) indexed all my media into itunes without copying all that over to my computer (defeating my original goal of saving space).
I realize this may not be clear, but whatever.
What you did was rebuild the library from scratch. Most people consider this as the absolutely least desirable solution to media collection transfer issues which is why I hadn't suggested it yet. In doing it you lose playlists, playcounts, ratings, etc.
Even if your media are disorganized from iTunes' perspective, if you still keep them in the iTunes folder you can still move it from drive to drive by copying the whole iTunes folder.