Diagnosis
Sticky liquid has seeped under the rubber button membrane and gummed up the micro-switch.
How to Fix It
Unplug the base. Use a cotton swab dipped in isopropyl alcohol (90%+). Press the stuck button repeatedly while applying the alcohol around its edges. Work the button to wick the alcohol underneath. Let it dry completely for 2 hours. This can dissolve the residue.
If That Didn't Work
The micro-switch itself may have failed. The button is part of a sealed control panel. You cannot access the switch without destroying the housing. The base unit must be replaced.
Heads Up
Wipe spills on the base immediately. Do not submerge the base in water. The button seal is not waterproof.