Gah, channel failure.
I had my iRiver SlimX 350 for the longest time (eh, well, had I not set it under my textbooks over days of time it might have lasted longer) before I began encountering a similar situation to your own player. I think the left channel, for me, failed often, eventually shorting completely. There was a time where I could fiddle the headphone adapter to create stereo, but this product is gone now.
The 1/8th inch audio adapter (TRS connector) of music players can be worn and damaged over use, or is poorly set from the start. Inside this adapter, conductive metal strips deliver channels to the headphones... so, these are ruined over time by the pushing and pulling against the headphone jack.
I know not of how to repair a damaged strip in question, so you're going to have to give back the MP3 player... I'll look up some more mechanics behind this device, see if there really is a way... but I'm doubting the chances of repair.