General:
* Broken
* Dead
* Finished
* Done for
* Out of commission
* No good
* Utter failure
* Beyond repair
Informal:
* Busted
* Croaked
* Kicked the bucket (informal, referring to death)
* Gone to pot
* Shot
* Worn out
* Down the drain
Technical:
* Inoperative
* Malfunctioning
* Defunct
The best synonym for "kaput" depends on the specific situation and the desired level of formality.