I'm not sure I understand. The path for the new storage location is One Touch (F:) and when I hover over one of the missing tracks in a playlist it says "File 'F:/__' is missing.
Also I don't have internet where I live so I'm typing on my phone and using muaic bee on my computer. Where I typed __' is missing it does say the song name and artist just how I have it saved on my hardrive. It's just really long to type. Since I can't copy and paste...
That makes it hard to give you specific answers to support you. A playlist is just a text file, with each line pointing to the path for each file, in the order your playlist was originally built.
When you moved the storage location of your music, the playlist directions no longer point to where those files are. So any player using that playlist has no idea where to look.
If you open your playlist file using something like Notepad or Wordpad, you will see each line with the first part that was the old location. Use the Find feature and enter that part of the path (easiest if you copy/paste from one of the files) then add the Replace info for the new file path. Choose Replace All and save the playlist.
Now your player should be able to find those tracks again.