The best way to see if what was the matter with him to cause death would be a necropsy but it may already be too late for that. I am not sure how long after death a vet will do this if it is not kept preserved.
Birds can hide sickness very well. It is not common in any way for a bird to fall from its perch breaking its neck, in fact it is almost impossible. They have been known to fly into objects at a high rate of speed (usually windows etc) and crush their air sac or become so stressed it causes their heart to stop. If your bird just suddenly died with no signs it could still be many things. It could be something as easy as stress or then again it could be parasites, a virus or many other things. There is no definite way to tell without a necropsy.
If you do decide to add another bird to your home at a later time I would either suggest getting a different cage or completely disinfecting the cage from top to bottom. Make sure the cage you have or get is large enough for the bird to thrive in not just survive. Make sure it is offered a healthy diet. Budgies can be very hard to switch to pellets and many argue that there is no need to switch them as long as they are offered a wide variety of see along with many vegetables, pasta, grains and fruit. Just a seed diet won't neccessarily kill a budgie but it does cause it to be in poorer health, it will sometimes shorten their life expectancy and many say it leaves them more open to viruses, bacteria, parasites and of course vitamin deficiency which can lead to eventual death.