How much storage can a 5th gen iPod have?

if the connector broke of the logic board, there are two (or three;-) solutions. One is to get another connector from an old logic board and have somebody knowledgeable with SMD components solder it on. The other way is to replace the logic board.

Now if you are really good and know how to solder etc. I suggest you check the answers on here SOLVED: The Brown connector broken. - iPod 5th Generation (Video) - iFixit It'll show you how to possibly fix the traces. Of course, your traces may look different and are not as or more destroyed. We would need to see what you are up against. Post some good pictures with your QUESTION so we can see what you see

Adding images to an existing question - iFixit Repair Guide