chances are that "bass click" is from a voltage offset at the outputs of the iriver. If you can, you should check with a voltmeter--if there's DC from signal to ground more than 30mV or so, it's probably not good for your headphones and you risk damaging them if you use them too long.
I suspect one of the passive components (DC blocking output capacitor, possibly, especially if they used a tantalum) has gone bad. Or maybe one of the ICs died. Unfortunately, either way, I don't know how you could possibly fix it without some electronics / soldering iron experience. . .
Or a better idea, see if the line-out still works.