Kksuns and Illusive are so right! Lots of research is required before purchasing any bird. A lot of people everywhere think that owning a bird will be like owning a hamster or a guinea pig, but the truth is that any bird takes a lot of responsibility. If you take good care of them, they can live to be 15 to 20 years old - parakeets, anyway.
I am sad to hear that your parakeets had to die so young. I am hoping that you can start over with your next one if you decide to do so. Many of us here may seem "crazy", but in all honesty we are just concerned about the bird's safety and health.
Keeping him/her by a window is not good and neither is carpet cleaner or any chemicals around birds. Also, Teflon pans aren't good either if your bird was by the kitchen. Teflon is also bad for humans as well. If your bird was looking "fat", then he was probably very ill. If you didn't know, parakeets require regular avian vet attention just like a cat or a dog. You should look up a local avian vet near you. If you can not find an avian vet, then call around to see if a clinic does birds - it's better than no vet at all, you know. : )
Update us on what you decide and how your research is going! You can educate your kids as well. You never know, it could be fun! Then, you and your kids can properly take care of your bird together. : ) Good luck!