This is the 4654th most frequent Turkish word.
bozulduğunu
"That it is broken" or "its breaking/deterioration."
Here, 'bozulduğunu' is used to indicate the state of something spoiling or being ruined, referring to the ice cream in specific.
Hava çok sıcaktı, bu yüzden dondurmanın bozulduğunu fark ettik.
The weather was very hot, so we noticed that the ice cream had spoiled.
In this sentence, 'bozulduğunu' describes the condition of the old device breaking or ceasing to function properly.
Eski cihazın artık bozulduğunu ve işe yaramadığını düşündüm.
I thought that the old device had broken down and was no longer functional.
Here, 'bozulduğunu' denotes the deterioration or decline, in this case, of relationships.