Does your budgie have any favorite foods, maybe millet or a type of fruit etc that it will always eat? Try to entice him with his favorite food. Also contact your avian vet to see if he/she will see him.

You might also try a "mash" type of food. Maybe oatmeal cooked and then let cool until just warm not hot or a sweet potato cooked in the microwave until soft, then add a bit of apple or orange juice and a bit of cinnamon to make really soft and mushy again feed when warm not hot. Sometimes a warm food offered on the tip of a spoon will entice a bird to eat.

If your bird is ill there is not much help in enticing it to eat unless your vet can diagnose the problem. Sorry I couldn't offer more assistance.