I just now joined the Forum to say thanks to all who've posted in this thread. I'd been putting up with the super-loud hum for far too long... until today. After reading the previous posts, I grabbed a soldering iron and two 100uf 35v 105deg capacitors from Fry's Electronics. First time I ever soldered anything, and it's a success! The hum is totally gone - I'd forgotten it could be like this
The only real issue I had was with removing the capacitors. I'd de-soldered as best as I could, and straightened out the tips poking through, but could not pull the capacitors free from the board. I eventually pulled the capacitors completely off of their pins, with the pins still stuck to the board. After that, it was a simple matter to de-solder the newly exposed side, immediately pulling the pins free. Attaching and soldering the new capacitors (noticeably smaller than the originals, huh) was pretty uneventful.
Thanks everyone!