Picked this up a few days ago. It's not working right now and it's missing some screws.

NOW I LIKE THAT A LOT !!! Different looking design very clean looking for newer model. I personally have 2 My My players.. like them.

Any ideas on where I might find the 4 little screws that are missing?

90's era small all metal bodies units. See if find on ebay not working or bad cosmetic condition player can buy for few dollars. Check photos enlarge as can see if screws appear somewhat like remaining ones on player they may fit.