HP 15c Limited Edition OLD batteries

[jebem]

Imho the batteries at 2.9V may already be depleted, as they have high internal resistance and when complex current load is imposed by the calculator processor (this model has nothing in common with the origin high quality high impedance low leakage current 15C) it is expected to see the voltage dropping below the value you reported (assuming you measured the cells with no load).

Basically I would use fresh good quality batteries to test the calculator.