"The key is broken" is correct. The accepted past participle for "break" is "broken."
The American Heritage Dictionary of the English Language gives these definitions for "broke":
broke (brÅk) v.
Past tense of break.
Nonstandard. A past participle of break.
Lacking funds: "Following the election, the Democrats were demoralized, discredited, and broke" (Thomas P. O'Neill, Jr.).
*The American Heritage Dictionary of the English Language, Fourth Edition.Houghton Mifflin Company. 2003