My pet parakeet just died and I don't understand why? Please help ='(!?

My sister and I had two male parakeets about the ages of 5-6 years old. About 3 days ago, a cat had come in through the back door and toppled their cage off the stool and to the ground, in an obvious attempt to kill them. My sister witnessed this just as it was happening and scared the cat away before any more damage was inflicted. She described the birds as being very calm and unharmed right afterwards, despite their cage being a total mess. However, about a day or so later, we noticed that one of our birdies could barely fly. He was always an adventurer and he liked to leave the cage and fly about the kitchen and dining room, but he remained on the kitchen floor and hallways, crawling about for a couple hours, unable to fly back into his cage. I noticed that he was able to fly about a foot or 12 inches high, but then would come crashing back down to the ground. We managed to get him back in his cage manually, thinking that his wing(s) would heal within a matter of time. A couple days later, which is today, I peered into his cage to find him lying face down on the floor of his cage, dead. The other bird was flying around like normal, but my poor other bird was smack dead. Confused and distraught, as he was otherwise a very healthy bird living in a fine environment, I put him in a lined box so we can bury him later today. I have not yet told the rest of my family- they are all still asleep. What do you think the cause of his death was? =(