Huck has the right idea in addressing faulty digital instrument feedback. GPS speed, corrected for wind and altitude, is another arrow in the quiver.
To sustain cruise in the absence of airspeed indications, apply a known/normal power setting and deck angle. Fuel flow, if available, works too. In addition, mechanical feedback/feel occurs with the onset of initial buffet on most aircraft.
I think you should disconnect autothrust as well, as FADEC, with erroneous input, can deliver erroneous output. Finally, it's good to know that TOGA is always TOGA, and IDLE is always IDLE.
There is a self-powered artificial horizon on all air transport certified aircraft.