DIAGNOSIS The red button is the circuit breaker reset. If pressing it yields no click and the mower is dead, the issue is elsewhere.
FIX Follow the power path. Step one: Unplug the mower. Press the red reset button. You should feel a definite click. Step two: Plug the mower directly into a wall outlet, bypassing any extension cord. Step three: Depress the safety lever and press the power switch. If still dead, check your household circuit breaker or GFCI outlet. Reset if tripped.
IF THAT DIDN'T WORK The power switch itself or the internal wiring may have failed. This requires a continuity check with a multimeter or professional service.
HEADS UP The red breaker button only resets if the mower is unplugged. It is a manual reset thermal protector. Wait 5 minutes after an overload before resetting.