Step 1: Open it up
When there's nothing obviously wrong, make disapproving noises and have your house-mate phone his brother to see if the brother still has an extra amplifier. When it turns out he doesn't, carry on to step 2.
Step 2: Vacuum out all the dust
Vacuum out all the innards. Wire it back up and be amazed that all the channels now work.
Step 3: Reassemble
Update: It has stopped working again twice since I originally wrote this, and both times vacuuming it out has fixed it.
Jan. 2008 - vacuumed, fixed again.
Feb. 2009 - vacuumed, didn't fix, vacuumed more vigorously and it fixed
Feb. 2009 - a week later it stopped working, and I vacuumed it gingerly, which fixed it.
There's no visible dust inside the amp. I don't think it's a loose wire because "pretend" vacuuming (or shaking for that matter) has no effect.
I posted a question about why this work here:
My integrated stereo amplifier periodically stops working. Why does vacuuming it out fix it?