First things first, check your headphones.

Or, even better, try a completely different pair of headphones.

I would very highly doubt that it has to be resoldered to the board

Why do you doubt this? I've seen that very thing happen on countless portable players dating all the way back to the Sony Walkman days.

And yes, twisting the plug in the jack can easily cause a loose solder connection to temporarily make contact, because it changes the direction of the stress against the assembly.