DIAGNOSIS: A completely dead button, while the machine might have power, often points to moisture or coffee spillage getting behind the button panel and shorting the contacts.
FIX: Unplug the machine. Wipe the entire top surface, especially around the button, with a dry cloth. Then, tilt the machine forward over the sink (with the water tank removed) and gently tap around the button area. The goal is to dislodge any liquid that's pooled inside. Let it sit unplugged in a dry, warm place for at least 24 hours to hopefully evaporate any internal moisture.
IF THAT DIDN'T WORK: If it's still dead after a full day dried out, the control board or the button membrane itself is probably faulty. There's no user-serviceable fix here. You'll need to contact Nespresso for a repair or replacement, especially if it's still under warranty.
HEADS UP: Be really careful not to overfill the water tank when inserting it. Sloshing water directly onto the button panel is a classic way to cause this. Always insert the tank slowly and deliberately.