Too late he died.There is no way for us to determine what the issue is, he may have an infection in the GI tract or he may have a problem with his liver, how long has this been going on, can you get him to a vet that treats birds? What I can tell you is that you need to clean the cage every day, that picture you posted of the droppings indicates a filthy and and unsanitary environment. Locating an Avian Vet//On-Line Avian Veterinarian Help
It would be a good idea to take your other bird to the vet. Since there's no way of knowing what was going on, and whether it is contagious, a vet can examine your other budgie to make sure its healthy. You can also request a necropsy be done on Leo's body, if you still have it. As Cody mentioned, the cage needs to be cleaned! The sooner you get your other bird to a vet, the better. If it is contagious the other bird may be more robust and has been able to fight it off so far, but in the end could get sick and die too. Even if the other budgie seems fine, it may already be infected, but is hiding it. So sorry about leo.Too late he died.