IMPUISSANCE: DESECRATE

The question asks for a word pair unrelated to the given pair.

Impuissance refers to something powerless, while Desecrate means to destroy something.

Option A: Decrepit means physically worn out, and Desolate means barren, or abandoned. Both words are formal and negative, aligning with the tone of "impuissance" and "desecrate."

Option B: Effete means a state of weakness and sacrilege means weakness in a sense similar to impuissance. These are again similar to the given words. 

Option C: Ornery means Bad-tempered, and Contort means to distort something.

Option D: Bedraggled means dirty and disheveled, while profanity means blasphemous language. This too is somewhat close to the given words.   

Of the given options, only Option C is not related to the given words and hence would be the correct answer.