My external hard drive doesn't read on dthe desk top but shows power is on what could be the faulty.have I lost all my music

The drive likely failed... just like when one fails inside your computer. External drives run hotter and are subject to being banged around.

I'd crack it open, see if by chance you might be able to see it as a second internal drive in your computer... odds are its not going to but it's a last ditch way without spending bigtime money on a data recovery which will cost way more than that music was worth.