Little update...

The problem indeed appears to be in the power supply. The rio will boot and work normally when powered by an ordinary ATX power supply (though the sound quality suffers greatly).

My meter shows that the PS puts out ~14.5v without a load, but drops to ~3v with the rio's logic board connected. Web research shows that power supplies based on the controller chip this one uses can fail in a way that causes them to cycle on and off as they try to start up. This would explain the blinking of the logic board's LED...which is constant lit when attached to a working power supply. The blinking is the power supply comming up to power but then shutting back off when the controller chip doesn't see any power from the output side of things.

Careful examination of the PS board has revealed that C15 (a surface mount capacitor) is chipped (as is visable, somewhat, in these pictures http://jupiter.okb-1.org/camera/public/RioBrokenPS/ ). I'm not sure if this is the cause of the problem or just collatoral damage caused by whatever else has failed.

As I can't find any markings on the capacitor in question, and don't have SMT soldering equipment, I am now looking around for a cheap but audio quality 12v power supply.

It's nice to at least know that the problem is indeed the power supply.