The files - mix of MP3 & FLAC - do not show unless All is selected. None of the files play, either.
This sounds very much like a symptom of the files themselves being corrupt, or a corrupt file system.
As saratoga stated prior to my post, Rockbox should (and does, in a normal circumstance) display any file format it has the ability to play (which is a lot...a LOT). Neither .mp3 nor .flac are "exotic" formats, and both should definitely be displayed in the File Browser with the Show Files setting set to either All, Music, or Supported.
I would advise you to use chkdsk (for Windows OS) to
check your disc for errors, on Linux you would want to use
fsck.vfat instead.
Hopefully, you have the media on the device backed up elsewhere, in which case data loss on the device is of little to no consequence. It is possible that you may not be able to fully recover all of the media on the device if the file system is corrupt. If you do have the media on the device backed up elsewhere you may find it is easier to simply format the disc and reinstall the Rockbox binary (the Rockbox bootloader and the Apple OF will not be touched - the Apple OF will recreate the directory structure it requires the next time the OF is booted, nothing that resides on the storage partition is essential to the Apple firmware).
[Saint]
EDIT: Pre-answering a question - "OF" == Original Firmware