My friend has the old Logitech Z-5500 5.1 System, and at some point, the front-center speaker stopped emitting audio. The problem was very obviously with the amp (plugging the corresponding 3.5mm plug into any audio source resulted in no audio in the speaker, but the speaker plugged into another channel on the amp worked fine). This sounds identical to your problem.
After pulling the amp out of the sub assembly, a quick peek at the board showed that the board is split into different sections, where each different channel's amp is in it's own little section. Likewise, each channel had its own fuse soldered to the board (and covered in heatshrink). Sure enough, using a DMM to check continuity on all the fuses, one of the fuses had blown. Desoldering the fuse and replacing it was all it took to get the center speaker working again.
The reason the fuse blew, I'd assume, is that at some point when the speaker system was on, the two wires going to the front-center speaker shorted, causing a zero-impedance situation and thus causing the fuse to blow. If you're comfortable with pulling the amp apart (leave it unplugged for a couple of hours/days, then try pulling it off of the sub), then I'd definitely recommend checking all the fuses for continuity, provided the design of that speaker setup is similar (which I would imagine it is).
edit: Below is a picture I found online of a shot of the main PCB of the amplifier in the Z-5500. Along the right side, you can see four glue-covered fuses (encased in black heatshrink) just behind the corresponding channel amplifiers (hard to see, but perpendicular to the plane of the image, attached to the heatsink). If you're daring enough, I'd pull the amp apart to this point and test continuity on the fuses (just need to poke through the glue with the fuses). There are also fuses on the left side that are a bit more difficult to get to, due to the wiring. If you do need to take out wiring, make sure to label it as you remove it (take pictures as you disassemble it too, if you can't remember where parts belong).