I had this same issue, and I think I may have another solution - it involves uninstalling Skype, though.
I have a first generation iPad with iOS 4.3.3, installed a couple of days after it was released. A couple of weeks ago I noticed that there was no sound whenever I used headphones or whenever the iPad was connected to my Jensen Rocker. As noted upthread, opening Skype and making a test call was the only thing that brought the sound back. The built-in speaker has always worked fine.
What I did was uninstall the Skype app and then I restarted the iPad by holding down the lock button to power it off (and turning it back on again). I then opened up the iPod app and played a song with my headphones and I just finished listening to it.
I hope this solution is helpful to some, even though it means going without the app because I don't think it's been updated since February. I should also note that the last time I used the Skype app (which was about a month ago) the people I called could not hear me. I think it might have something to do with iOS 4.3.3, because it worked fine before I updated the iPad.