Your MP3 player will probably continue to work as a data medium if it uses flash memory as this retains data without power -- operation when you insert it into the USB socket is powered by the USB circuitry of the computer.
If the device is no longer working as a music player, try using Windows tools to check it as a drive. Insert the unit, when it appears as a drive, right click and select Properties then Tools and Check Now (don't select automatic repair). This may fix the issues but you may lose some data -- so first transfer any data you must keep onto your computer hard drive.
In a worst case scenario you may have to reformat the player (again in Windows, select Fat32 not NTFS). But first check that you have a copy of the player's firmware and utilities (usually on a CD supplied with the player) as you may have reflash the firmware back to the player.
my mp3 has recently stopped working...however, thats not the problem since ive bought a new one
the rechargeable battery on my broken mp3 still works and recharges, so ive found a good use for the mp3 to use it as a data storage device (usb drive)
but my question is: can the mp3 still work as a data storage device if for example, the battery goes dead