I assume you have also tried another headset to rule out the possibility that your current set or earbuds are not damaged or faulty in some way?
If so, you likely have a hardware issue with the device. A restore to factory settings would have corrected any sort of software glitch or error caused something such as corrupted data.
You'll want to either take or send your iPod in for service/repair.
Not sure exactly. It could be the iPod's actual audiochip that is soldered onto the logic board in which that would be a somewhat expensive and difficult fix.