How can I replace a broken headphone jack on my iPod?

it could be a lint inside the headphone jack or in the worst case - a loose/broken connection of the headphone jack.

the first thing i would try is to look into the headphone jack - and signs of "dirt" inside ?? - maybe you should blow into it (some people use canned air for that)

if nothing helps - it's possible that the flex cable is broken (they break pretty fast)

you can replace the part - but soldering is necessary!!

use the logic board guide - you can see the part in step 9.

but soldering some wires to it is also possible....