My iPhone music library has a lost of songs, but in iTunes is shows nothing on my device.

Having re-read your post, it sounds as though you have synchronised your phone with a new iTunes Library (on your new computer).

However, Sync is one-way; from iTunes to the device. This means that the Sync will have removed all the music from your phone and (if you set any Sync options) added onto it only what is in your iTunes Library.

The first question therefore, is do you have your music in your new iTunes Library?

• If you don't, you need to import the music from your other computer or backup to your new library. In the case of iTunes Store purchases, once you sign into your account in the new library, you can download the purchases from the store to your library.
• If you do have your music in the new library, set some Sync options (on the Device/Settings/Music pane) in order to add it to your phone:

and then

If you use Sync Entire music library, (3.), the options in 4 are not displayed.

Your first screenshot shows your device, while the second one shows your Library (not your device). Note also that the Music Playlists heading is what is on your computer, not what is on the phone.

However, it looks to me as though all the music listed in your Library is not actually on your computer; it's in the cloud, as denoted by the cloud symbol to the right of each song. To download the song, you need to click on the cloud icon. Is this music purchased from the iTunes Store?

I don't use this feature, so I have to make a best guess: I think that if you select all the songs you can then click on Download and iTunes will do the work for you.

• • in your library (not the device), use the Songs view
  • click on any song (so that the next command works)
  • click on Edit / Select All on iTunes' top bar menu
  • click on Song / Download on the top bar menu

With any luck, that downloads all the songs into your library

Once the music is on your computer (and plays on your computer), connect your phone to iTunes and select the Device / Settings / Music pane (1. in the screenshot). Make sure to click on the phone icon at the top (as indicated in the first screenshot in my first post) and then click on the correct Music heading (1.), as indicated in my screenshot:

• once on this pane, click the Sync Music button (2.)
• in (3.), if you select Entire Music library, all the music in it is added to your phone and you will not see section 4.
• (section 4. only appears if you choose sync selected playlist, artists, albums and genres. That's a useful feature if your device does not have sufficient capacity for all your music)
• tap the Sync or Apply button for these changes to take effect

You're making progress.

First of all, the iTunes iTunes Media Folder Location is for new CDs that you rip. It will not cause iTunes to look there for existing files. That said, it is useful to set it to the same place as your existing music, so that any new CDs that you rip are stored with the rest of your music files .

The Add Folder to Library command does (as you've found) add the files on your computer to your Library, so well done.

Regarding the fact that you have duplicates, I'm not sure why that happened, but have a read of this tip from fellow user turingtest2, which should help you: Duplicate songs in iTunes - Apple Community.

I asked our hosts to remove your first picture as it contained your personal information (in addition to the serial number of your phone).

If you need to post that image again, please ensure that you blank out any personal information. Look carefully at your copy of it, I'm sure you'll see what I mean.

the fiend