Your player is fine, else it wouldn't have worked without the cap. I bet that the charger chip is bad. It is that quadratic chip, 5 pins on 2 sides, 2 pins on the other 2 sides. On my picture, it is just below the power connector. It is a Texas Instruments chip, you can find detailled infos on:
http://www.rockbox.org/twiki/bin/vie...wareComponents
If you can't replace it yourself, maybe the repair shop will be able to do it. We know more about the Iriver hardware than they do
If you follow the link to Texas Instruments on the rockbox link above, you can download the data sheet and select the appropriate part number. The chip in the iriver is an AZU... you can even order it directly from TI. I know that replacing SMD components is not easy... you need a solder iron fine like the tip of a pencil, a big magnifying glass mounted at your table, and a steady hand.
Horst