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Try removing the batteries, and leaving the device on a (dry, non-humid, non-dusty) shelf for overnight. Then put the batteries back in and try the device again.
Then try cleaning the terminals in the battery compartment, after removing the batteries, first by rubbing off with a fresh pencil eraser, then by wiping the terminals off with cotton swabs moistened in rubbing alcohol, then letting them dry off for 5+ minutes with the battery compartment door open, then try turning the device On again.
Let me know how it goes. I may have more advice to offer, depending on results etc.