Okay, let me put it another way.
I’ve got an MP3 sitting on my desktop and it’s playing in iTunes on but whenever I move the original from the desktop, it stops playing even though I’ve tried to drag and drop the MP3 into iTunes to copy it there.
Music is added to an iTunes Library, not copied to it. When you drag and drop you are not copying the file into iTunes. Instead, you are telling iTunes where the music file is (i.e. on your desktop) and that is the file that iTunes will use.
Consequently, when you "move the original", that is not what you are doing. You are in fact moving the file that iTunes is using, which means that iTunes can no longer find it, therefore it cannot play it. The same thing applies if you delete it; you are in fact deleting the file that iTunes uses.
The advice I offered previously was to move the file from your desktop to the folder that iTunes uses to store its music files before you add the song to your iTunes Library. (There are a couple of methods to do this, we can discuss them later if you wish.) In other words, only add the music to iTunes after moving the file. That keeps your computer tidy, but more importantly, it means that when you need to move all your music to new computer (which you will, one day) it will be a simple job because all your music will be in sub folders of iTunes.
You can use the tip that tt2 has mentioned. That is, turning on an option in iTunes that causes iTunes to make a copy by itself and to use that. If you use that method, then you can move the original file. However, where you move it to is important. You should be making a backup copy of your music (in fact, of your whole iTunes Library) so that if - or when, your computer's hard drive fails, you will be able to use the backup to recover your music.