The correct answer is C. The sentence "Hidden under the doormat, the burglar easily found the spare key" contains a dangling modifier.
When a sentence has an introductory phrase, it should apply to whatever is immediately following it. Therefore, the setup of this sentence implies that the burglar was hidden under the dormat. Of course, this cannot be true. That's why this modifier is incorrect.
A better way to write this sentence would be: "Hidden under the doormat, the key was easily found by the burglar." With this revision, the introductory phrase clearly modifies that which follows it.