iPod: how to solve: sceen shows lines only (nano 2nd gen)
Eventually, Apple Community Specialists recommended that I contact Apple Support. They said this is definitely a display fault and it needs exchanging; however Apple only provides support for devices for about five years and they have no spare parts available as of today (2016), thus recommending me to source spare parts from vintage devices.

UPDATE: I've purchased a replacement display from Hong Kong via eBay and implemented it following this guide: https://de.ifixit.com/Guide/iPod+Nano+2nd+Generation+Display+Replacement/421 (works, but new display has no backlight) - when attempting to slide the board back into the housing, it didn't fit - only after I widened the case with a spudger. Seems like it once had gotten crushed, causing an issue with the display connector. I've later re-implemented the original display - works as well.