Use a heat gun to melt the solder and the old connector will Almost fall right off the board. Just tap it with a screwdriver when it starts to come loose. Before this, of course, remove the board from the iPod So you don't melt everything on the board.
Actually there's a very simple way to remove the old connector you using A heat gun. You can pick one up for about 25 or 30 bucks at a hardware store. Disassemble your motherboard from the rest of the iPod put it in a clamp and use the heat gun on that connector back and forth on the metal parts in the connector. When it gets hot enough, the solder will melt and the connector will kind of droop. When it does that, Tap lightly with a screwdriver and it'll fall right out.
I had a similar thing happened. The solution for mine was to reattach the digitizer connector in the iPod. The digitizer connector is the one under the motherboard not the one on top of the motherboard.