Hi sugarplumsss,
Tyros4 can only work with a maximum of 500 files per folder. So you have to divide (move) the MIDI files into folders/subfolders on the computer and make sure that the stated maximum number of files is not exceeded. However, it is best to only work with a maximum of 100 files per folder. In addition, the length of the file name must not exceed 41 characters (including the file extension and, if present, the Icon ID, max. 50 characters are allowed).
By the way, with so many files, I would not initially copy all the files to a USB stick or the Tyros hard drive, but first play them back from the computer over the Tyros via USB-MIDI cable. Under Windows I recommend the programs "vanBasco Player" and (for managing the MIDI files) "PSR MIDI Database". There are certainly suitable MIDI Player programs/apps for the Mac that can output via USB-MIDI. You could also use a DAW such as Logic or Cubase, but a simple MIDI Player app would probably be better here if you're just looking through lots of MIDI files quickly.
Best regards,
Chris