Hopefully this is not a redundant post, but since I wasted a week and numerous phone calls hopefully this saves some of you the same.
I have a 160GB iPod classic. It is just over a year and a half old. Use it regularly in the car, working out etc. It recently started having static come from both the headphone jack and apple dock connector. I perused the forums and tried various things to no avail. Apple seemed to have no idea about the problem (or would acknowledge), and I was left with chucking it in the trash.
Now to the fix...found a soldering expert at a local repair place. He did the following and was able to fix the issue.
1) Apple uses Infrared solder which is not as flexible as the older electrical grade solder. As a result, if you leave in extreme heat too long (i.e. in a car), the solder balls that bond the audio processor can heat up and crack (causing the static)
2) The solder expert was able to "reflow" the audio processor, here is what he said he did...
Put a little kester no clean flux in front of the audio processor blow it under to help clean out the area
Heat up the processor to approximately 211 degrees Celsius. His advice was to never go above 230 degrees
Let cool down, so soldering balls reattach, do not push down on the audio processor.
3) That was it. $45 later I have my iPod back!
***NOTE - I am not a technician, and would not rely on my advice alone. Check with a local iPod repair shop to see if they know how to do this and can assess if this is your issue as well. I don't want to be responsible for any further damage to anyone's devices : )