Ram, sorry but I have to ask. Did you double, triple check to make sure that all connection make good contact? Does the hold switch work? I would think that yes, it is possible that you can hear the sound through the dock connector. I seem to remember years ago there were some issues like that and it was suggested to press on the bottom right of the iPod to see if the sound returned, and it worked for most of the people. The reason for that is assumed to have been a bad solder. If you open up the iPod, the big chip on the bottom right (where you would be pressing from the front)... ie. the big square chip sitting in the corner is the audio decoder labeled P5021C-TDF. This chip isn't attached properly to the logic board, obviously it works itself loose over time. You get sound when you press firmly on this chip - which is effectively what you are doing when you press on the bottom right corner of the Ipod.
Anyhow I woulds check on the connections first make sure all that is looking good. I would even consider redoing the audio jack. Oh yeah and don't forget to try a system restore through iTunes. Good luck