If Beethoven were alive nowadays he would write a fourth movement for his "Piano Sonata No. 14" (erroneously known as Moonlight Sonata)...

but that´s sad to listen to, I think. Powerful but a little bit sad.

She inspires happiness indeed, not sadness. But I think he would compose something sad because his not correspondant love was what inspired him to write so beauty, although sad, melodies.