I tried removing the tip (the bit that broke and is lodged in) by digging at it with various small tools but it did not budge. Is there an easy way of removing it or even replacing the jack with a new one?
Look for the appropriate tutorial on how to take your iPod apart. There might be a way to get it out once you are inside. Otherwise hunt around and im sure you'll find a replacement jack online you can put in.
I made a video that covers basically how I fixed this without you being required to buy replacement parts or RMA or do anything of the sort. I uploaded it to youtube. Basically, you only have to spend ~$4...
happened to me recently. the tip came off cleanly so i saw there was a recess in the remaining part of the jack. when i looked in the socket i could see the tip, there was the metal stub in the center which would've fitted in that recess in the jack body. so i just put a *tiny* amount of superglue in the recess & plugged it into the socket normally & held it down a few seconds. was able to retrieve the tip on the end of the jack & there was no superglue around the join or inside the socket. phew! headphone jack was finished though.
You wonderful techies! It worked on the first try. I used the remaining part of the broken jack because I figured the two broken pieces would have a closer fit. I put a tiny amount of superglue on the remaining part, scooped out any excess with a toothpick, stuck it in the port on my iPad, and didn't leave it in long enough to really do any damage by gluing the whole thing inside the iPad jack. I waited about 3 seconds before I pulled it out. Lovely! Thank you!