So your media are on the external drive and your library files are on the internal? iTunes is a bunch of files, not just your media files.
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
iTunes 9 [and later]: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847
If your library files are on your internal drive you need to copy the iTunes folder from Home > Music to the same location on the new computer (make sure you don't mind replacing the one already there), then start iTunes. It may want to update your main library file.
If instead of what you say, the whole iTunes library is on the external drive:
iTunes: How to move [or copy] your music [library] to a new computer [or another drive] - http://support.apple.com/kb/HT4527
Quick answer if you use iTunes' default preferences settings: Copy the entire iTunes folder (and in doing so all its subfolders and files) intact to the other drive. Open iTunes and immediately hold down the Option (alt) key (shift on Windows), then guide it to the new location of the library.itl file in the moved iTunes folder.
That looks like a real mixture of files. This is how things should appear:
For example, there should not be a media folder inside of your Previous library folder, but from the bare glimpse I get of the size column it looks like it doesn't contain much. Unfortunately your screenshot doesn't reaveal your whole iTunes folder, just the previous library section, so it is hard to tell if you in fact do have all the bits and pieces.
Okay so below is a pic of all of the folders and how it's laid out. The itunes folder sits in a sea of thousands of folders of albums/bands.
Everything you see there is all there is. Is there a way to delete these itunes files and make new ones?
I notice now you were likely using a much older version of iTunes on your old computer. Still, one of the links I provided shows the structure of older iTunes folders and files as well as the new one (iTunes 9 and later).
I am seeing all kinds of non-conventional things in your files and folders. iTunes Media and Automatically Add To iTunes do not belong in the Previous iTunes Library folder. You are completely missing a valid iTunes library file which is the central controlling file for all iTunes. It should be in the top level iTunes folder and should either be called "iTunes Library" (no extension) under old versions, or "library.itl" with newer versions. You have neither. Your .xml version of the file also does not have a valid name (you cannot rename them or iTunes will not recognize them). The .xml file hasn't been updated in 6 years anyway. The bottom line is, this is not a functional iTunes folder. I also do not see any of your media unless it's those other folders at the top level of the screenshot (I don't know if those are bands or what).
I cannot check your computer myself so you will have to familiarize yourself with the iTunes folder structure in the links I provided earlier and hunt for the correct folder yourself. It certainly isn't the one you are showing me. One possibility is you kept just your media on the external drive but all the other files and folders that make up your iTunes library are still on the main drive of the old computer. That doesn't explain why any of that kind of file is on the external drive but that's an aside.