Chosen Solution
I prematurely replaced the headphone jack thinking that was the problem - which didn’t work - and then realized it also won’t output through the docking jack to my stereo. Yes, I dropped it.
sounds not good. i answered to a similar problem a few days ago. i qoute myself ;-)
a common problem are shot capacitors on the logicboard (c145 & c146). you can see them in step 8 of the logic board guide. the two orange parts are sometimes defective/shot/burned. they are 220µF capacitors and if they are “bad” they could look like this:
it could also be a problem with the P5021C-TDF - this part is the black one, left from the burned piece on the image above the solderings of this chip failed on many 5g iPod’s in less than a year - if you want to read more about it: CLICK here if you open your iPod (enough to reach the black chip i mentioned) - and play some music - try to press slightly with your finger in the back thing - now you should hear the music