Chosen Solution
headphone connector not connecting completely, sound in one ear only
The iPod classic is extremely difficult to open, but it is possible to be done. Here is the link to the repair on iFixit: iPod Classic Headphone Jack & Hold Switch Replacement You have to buy the correct part, either a thin or thick, depending on your model. Good luck!
A common problem. It’s either just a bad set of headphones (best case) or the headphone jack in the ipod is damaged. One of the contacts could have been bent so that it no longer connects with the plug. If you are like many people, you may leave your headphones connected to your ipod when you store it in your pocket or a bag. Pressure on the base of the plug can force the tip of the plug into one side of the inside of the jack, deforming it. I don’t know of any way to fix the jack, but it is a cheap part and is easy to replace.