- Try another cable. Some 5G iPods were shipped with Lightning cable that were either initially defective or failed after short use.
- Try another charging source
- Inspect the dock connector on the iPod for bent or missing contacts, foreign material, corroded contacts, broken, missing or cracked plastic. Yes it is likely that the post was damaged by pulling out the plug.
- Make an appointment at the Genius Bar of an Apple store.
Apple will exchange your iPod for a refurbished one for this price. They do not fix yours.
A third-party place like the following will replace the connecto for less. Google for more.