Why is my iPod not charging?

I have a white 30 GB iPod video classic that I bought used a few months ago. It was working fine at first, but now it is not recognizing any of my charging cables that well when I connect it to the wall or to my laptop. I was using my old iPhone 4 charging cable that was working fine. It charged normally and it synced to my iTunes normally. Then the connection started to go in it out, causing the iPod to eject itself from iTunes and stop its charge. I used some other iPhone 4 cables that I had, but the same thing still happened. Since these cables that I had were very old, I decided to buy a new one online (not Apple brand), but this one didn't work either. I went back to the original cables that I was using, and it does the same; the connection will go in and out and then it will simply not recognize it at all. Every time I connect it with the cable, the screen of my iPod will light up, but the battery bar won't show that its connected or charging.

I read a few forums on this issue, and some said the battery needs to be changed (which I originally planned on doing because the battery doesn't hold charge for very long), while others said that the logic board needs to be changed because it could be a processor issue (which is a bit more expensive to replace).

Every other function of my iPod is working perfectly fine; the only issue is with charging and syncing it. What exactly is the problem with my iPod?