As soon as I safely remove from computer, it won't play the music I've downloaded onto it
What type of MP3 player is it?
I have had this problem with some of the MP3 players I have for my younger sons, i.e., non-iPod devices. Sometimes the player can only handle certain types of audio files, e.g., WMV vs MP3, and only within a certain range of compression, e.g., a MP3 at 256kbps might be outside of the range.
If you can provide the model of player, and then the information about one of the files that does not play I might be able to help further.
Also software you are using to transfer files and the operating system you are using would help as well.
So many factors, I know.