I assume you've checked different headphones/spea
if so, one other thing to try would connecting to some audio output device via the dock connector (speaker dock, car adapter etc) -- if you have such thing available. if sound comes out via dock connected speakers then at least you know it's not likely a logic board problem.
otherwise it's probably your headphone jack. you can find the repair guide here
before purchasing a replacement headphone jack, you might first want to confirm that the ribbon cable securely connected to the logic board.