When a parakeet is sick, i usually will hide it's sickness as long as it can (survival thing). Sorry this list is so long. It was to hard to summarize.
Unusual Droppings: The color of your bird's droppings will vary slightly depending on what you feed him. Nonetheless, you should watch out for droppings that are yellow, rusty brown, or tarry black. These can be indicators of internal bleeding, amongst other serious problems. You should also notice if there is a major change in the consistency of your bird's droppings. If they are too runny or too firm, it can cause complications for your pet.
Ruffled Feathers: Birds that sit with their feathers fluffed out for prolonged periods of time are often affected by respiratory problems or other disorders. Ruffled feathers are also good at concealing weight loss, which can be life threatening for a bird. If you observe this behavior in your pet for more than a day or so, you should contact your vet as soon as possible.
Red, Inflamed, or Runny Cere: Your bird's cere is what we perceive as his nose -- the little patch above his beak that holds his nostrils. Pay close attention to your bird's cere. If you observe any redness, inflammation, or discharge, there is a very good chance that you pet could be seriously ill. Make sure to keep your bird wrapped up and warm on the way to the vet.
Cloudy Eyes: If your bird's eyes look cloudy or have a discharge coming from them, he may be affected by a respiratory, nervous, or muscular disorder. You should rush to the vet as soon as possible as your bird needs immediate treatment.
Reduced Appetite: Birds have extremely high metabolisms, so it is vital that they receive adequate nutrition every day. If your bird stops eating and begins to lose weight, it may be a sign of an intestinal blockage or impaction, in which case he could die very quickly without medical attention. Make sure to clean out the bottom of your bird's cage every day before you feed him. This provides an easy way to monitor food consumption, not to mention changes in droppings.
Open-Mouthed Breathing: Respiratory problems are among the most common bird illnesses, and unfortunately the most serious. If you see your bird breathing with his mouth open while at rest, there is a good chance that he is not only sick, but has been for quite a while. This is one of the most serious symptoms of illness in birds, and requires immediate veterinary attention, with probable hospitalization.
Dirty Feathers: Birds are, by nature, hygienic animals that bathe often and preen their feathers daily to keep them clean. If you notice feathers around your bird's face or rump that appear messy, clumped up, or stuck together, it is an indication that your pet could be sick. Food consumption and droppings should be monitored closely for a day or so, and any changes noted and relayed to your vet as soon as possible.
Weight Loss: Many sick birds ruffle their feathers when they don't feel well, effectively concealing any changes in body mass and loss of weight. Weight loss can be devastating to a bird's health, not only in terms of reduced strength, but inhibition of organ functions as well. Weigh your bird regularly so that you will know if your pet is having trouble maintaining his weight.
Tail Bobbing: As with many common signs of illness in birds, prolonged and repetitive bobbing of the tail can be indicative of a respiratory infection. Unlike people, birds lack a diaphragm to separate the chest cavity from the stomach. The muscles located at the base of the tail help birds breathe by playing a part in expanding the lungs to take in air. If a bird is having trouble breathing, the tail muscles will work harder, causing the tail to bob up and down. Tail bobbing is often not noticeable until later, more serious stages of illness, so if you see your bird behaving in this manner, report to the vet immediately.
Changes in Vocalizations: Much like humans, birds who don't feel well often become less talkative than usual. Pay close attention to your bird so that you can learn his normal vocalization patterns. If you stay in tune with the way your bird behaves, it's possible to pick up on clues to that way that he feels. If you notice any changes in frequency or general tone of your bird's vocalizations, he should be monitored for additional symptoms for the next few days. It is always better to be safe than sorry.
I hope this information was helpful to you. Sorry your parakeet died. It hurts to lose a pet.