How do I get iTunes songs which were downloaded from external back-up drive to play on new computer and is there a way to get my play lists back?

Question

When I try to play a song from my re-installed iTunes library, I get the error message:  "Song xxx could not be played because original file could not be found.  Would you like to locate it?" > "Locate" or "Cancel."  When I click on "Locate" I can't figure out how to get the song to play from any of the places that were "located."  The path is C:\users\Janet\libraries\music\iTunes
However, iTunes songs chosen from my library will play in iTunes (current version) when I have the external back-up drive plugged in!  I recently copied my backed-up iTunes library from my external back-up drive to a new computer.
Most of the songs, but not all, magically appear in Windows Media Player and I can play those just fine. 
I can see my iTunes library in the newest version of iTunes, recently downloaded to new computer, but can't play songs without connecting to the external back-up drive - so maybe there is something else on that external drive that needs to be on my C: drive? 
I am using an HP Pavillion Notebook, Windows 7, 64-bit.  My previous computer was Windows Vista.  Before Vista, I had XP. 
Back when I had XP, I wanted to purchase some songs to download to my computer. Because iTunes had the ability, I used it to create a massive library of songs, most of which were ripped from my CDs.  I don't have an iPod and iTunes worked fine for creating playlists and then burning them to CDs. 
Also, I'd like to know if there is a way to get back my playlists.
And another thing - in the older version of iTunes, there was a folder in the lists on the left-hand side of the screen where I could click to see all the songs I had purchased.  I'd like to get that ability back if possible.
In hindsight, iTunes was probably not the best choice for me to build my music library in a Windows operating system, but it seemed to be the best choice at the time.  I really wish I could convert all the songs to mp3 format.
I have been working with computers since the days of DOS, black and white screens, and no mice.  The first computer I bought for my own use at home was a Mac and it had "Flying Toasters" as a screensaver.  (I miss that screensaver.)  It did not have a tower and I believe they called it a laptop, even though the thing was as big as a suitcase and probably weighed around 30 pounds.  However, I am by no means a computer expert.  In other words, pretend you're trying to tell your mother how to do what I am asking. =)
Many thanks in advance to anyone who can help me.

Answer 1

I copied the iTunes file from the external drive and it's in both places.  I thought all I would need is the iTunes program (which I downloaded to new computer) and my iTunes library file.  There must be something else that's missing.  My iTunes library looks the same on the new computer as it does when I open it on the external drive.  If I click on an iTunes library song from my new computer, it will only play if I have the external drive plugged in.
My back-up drive is a mess.  I have multiple copies of music, video, photo, and document files and I don't know how that happened. ={  Obviously, I don't know how to back up stuff properly and there are back-up files extending over a 6- to 8-year period.  I think all I did was just drag and drop the main folders from the back-up drive to the same main folders on the C: drive.  Also (and I'm kind of fuzzy on this) Windows used to automatically save music files in a folder within my document files (which makes no sense to me).  As my Jewish friends would say, "Oy Vey!"