This is a documentary on Beethoven:
http://www.youtube.com/watch?v=dR2Os2pH2UA

What is the song that starts playing at 8:30 mark?

Wow, that's tougher than i thought.
It could be something from Missa Solemnis. I wish I could have looked it up by hummng it like that iPhone app.

Good call. It's from an instrumental section of the Sanctus from Beethoven's Missa Solemnis

It starts at the 4:15 mark of this clip, right after the big choral part:
<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/ckhnpg_m390&hl=en_US&fs=1"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/ckhnpg_m390&hl=en_US&fs=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

All written at a time in his life when Beethoven was completely deaf.

Nice work, HUG-H and dhmac. I performed the Missa years ago but would have been hard-pressed to identify it from that excerpt.

And yeah, if only Shazam worked that way.

Beautiful stuff! I need to hear the piece again, it's been a while!
And thanks for that clip of Lenny B. conducting! That's awesome!