The rice-drying appears to have resulted in success! I left it in there for a couple of weeks. When I pulled it out it would not turn on. I plugged it into power and it fired up immediately, even showing about 2/3 battery. After that, there was some odd behaviour - basically it would not turn on from a powered-off state using the power button. I set it to only sleep, never power off, and it's been fine. The weird part was that the power button worked to take it in and out of sleep mode, and even power off, but not power on. Today, after charging it from a completely flat battery, I decided to try the power-on again, and now it works. Seems all is well.