While I'm not " a 777 engineer or pilot", based on the available documentation my understanding is that the following happens after flame-out of both engines due to fuel exhaustion:
- all generated electrical power is lost, leaving only battery power,
- on battery power pitot heat is lost, the fly-by-wire flight control system (FCS) considers the airspeed unreliable and reverts to secondary mode,
- in FCS secondary mode envelope protection, turn coordination and TAC are lost, and the autopilot disconnects.
- the APU starts automatically and provides electrical and hydraulic power, until it too flames out when the fuel remaining in the supply line is exhausted,
- the RAT deploys and provides electrical and hydraulic power, restoring pitot heat and allowing the FCS to return to normal mode,
- with the FCS in normal mode the AP can be re-engaged by the pilot.
Standing by to be corrected by someone more competent than I am ...
P.S.
Here is another simulator "test" for comparison:
Geoffrey Thomas reporting Flight MH370 simulation