I'm sorry Yasmine, I must have been looking at someone elses profile that said they were from "England"...In the US, pets are considered personal property, just like a TV set or a car, so law-enforcement won't do much about it, except that they can give you the name and phone number of the correct animal-cruelty organization to call, so I'd call your local police department or sheriff's department, whatever police department you would call for anything else (the non-emergency number), and just ask them who you should contact locally to report animal abuse and neglect, and they'll be able to give you the phone number to the place you need to call...Then call them and give them the entire story of what happened. They probably won't get in any kind of legal or criminal trouble, however the local animal cruelty organization that you call generally will make a visit to their home or at least a phone call to let them know that purposely not feeding any animal that they buy is actually legally considered to be no different than "Animal Abuse" as a criminal charge, and that they could be charged criminally with a misdemeanor if they do it again. There is no such criminal charge as "Animal Neglect" in any state in the US, because "animal neglect" is considered no different than "Animal Abuse", so neglecting to feed a pet is considered no different than beating or physically harming or killing an animal. It's all the same charge, and it's taken very seriously...In most states they can only charge people with Animal Abuse if they are either physically harming their pets, or if they are failing to provide "basic needs" to the pet: food, water, and shelter at all times. And that's exactly what your neighbor failed to do, so they did break the law and could be charged with Animal Abuse.
I don't know if your area has a "Dog Officer", who is a part of the local law enforcement, but that's probably who the police department will put you in touch with if you ask them who to report animal abuse to. The Dog-Officer is actually a law-enforcement agent, and they will assess the situation and then they make a choice as to whether or not they go to a local judge and ask them to issue a warrant to charge them with animal abuse. That's usually how that works. In this case they may or may not decide to charge them, but if nothing else they will put the fear of God in them so they don't do it again, which I'm sure they will do unless they are threatened with criminal charges in the future.
I have no idea why adults would go out and buy a living creature for their very young child and think it's okay to not feed the poor thing, I guess they just thought it was okay to buy the poor bird just to shut their child up and stop him from crying, and then they'd just let the bird die, which they think is okay to do as long as it shuts their kid up...Obviously they aren't very good parents either, so they certainly shouldn't have any pets. If you have a local pet shop like Petco or Petsmart, that's probably where they bought the Budgie, they both sell Budgies and always have plenty of them for sale, and they typically don't care at all who they sell them to, they just sell them. It's hard to do anything to stop them from selling them to them again, so you have to go the law enforcement route.