Once I opened it up, it looked like this:

The problem with mine was that the one of the two orange ribbon cables was too loosely connected to the iPod’s circuit board.  Refer to the image.  When the iPod is freshly opened, the hard drive (the blue thing) should be covering the circuit board.  As noted in the picture, the orange ribbon goes through that little gap.  What I noticed is that as I wiggle around that cable, my left speaker would start playing sounds.  Once I found the “sweet spot”, I immediately stuffed cut up bits of a rubber band into the gap until I could jam up that spot well enough to prevent the orange cable from moving.  I don’t have a picture of what it looks like after it was fixed, and I don’t really feel like grabbing the screwdriver to open it up again.

UPDATE (Jan 5, 2010):

This is what it looks like fixed:

Notice the two bits of green rubber band filling up that slot.