Many of his works were written whilst going deaf, or after he had completely lost his hearing. As a musician, this was incredibly hard for him, however with the help of the amazing community that surrounded him, he transformed his suffering into works of incredible depth and joy.
I love the way his music has this sombre feel and speaks to the dark parts of life, and yet always has hidden in it the seeds of joy, which burst out into incredibly uplifting passages.
So, not only is it amazing that Beethoven could write at all while deaf, let alone the complex works that he did compose, but I love the way he held on to joy. His faith was so deep that he had a source of joy that was totally independent on the events of his life, and he desired above all to bring that joy to others. Pretty inspiring.
Here is a symphony (number 9) he wrote near the end of his life. I think it shows how he put the honesty of his struggles and the fulness of his joy into his music (it includes the famous "ode to joy").