If you can hear clicking, I think that the click wheel is probably working. The display has probably failed. You can get a replacement fairly cheaply on ebay. Be very careful when disassembling,the ribbon cable that connects the display to the main board is very fragle, and has probably gotten wet. I would use some isopropyl alcohol on the connector and cable before taking it apart. I have seen the gold traces peel off the ribbon cable when disconnecting it, rendering the display useless, so be cautious!
Do you mean the connector on the headset board? If the new cable fits in the old connector, then the cable should be fine. Did you make sure the little black bar on the new connector was in the up position?
The water tends to corrode on the click wheel connector. Use the guide to the point where you push the main board out. That will expose the connector. Carefully disconnect the connector, and use a little isopropyl alcohol on the exposed pieces to clean it.
Was the replacement headphone jack new? I have seen several iPod videos with your problem, and the new jack always solved it. Take a look at the ribbon cable connector for the main board as well, might have something covering one of the contacts.