Possibly misguided theory
As I noted in my last post, I'm not a pilot, so feel free to take this with a grain of salt...
IMHO, the evidence doesn't seem to point to any sort of fuel or other engine problem. For both engines to stop responding to throttle input sounds much more like a problem somewhere in the FBW path.
So here's my theory/question... If the computer thinks that the a/c is in an overspeed situation, would advancing the throttles be "ignored"? I haven't heard anything about alarms (such as overspeed) in the cockpit, but what would happen if somewhere in the electronics, an overspeed sensor/algorithm malfunctioned? Is it possible that this would interrupt the throttle commands from both a/t and manually advancing the levers?