Likely something in a local voltage regulator circuit. LED status is used as fault indicator in the field notice, so no total power loss. No console output at all likely means no power to the CPU.
I do not think that the actual powersupply itself is affected, I would think that would be said in the field notice. Also that would be an easy fix, assuming a separated power supply module. I never encountered a cisco ASA, but those separated modules are common in networking gear.