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Devices like this can fail for a number of reasons. One of the main ones is, surprisingly enough, sheer age.
How old is your Sangean radio? (measured from its date of purchase.)
If it was exposed to low or high temperatures while being operated or being powered On, that can contribute to eventual device failure to operate.
Also, a thing to check on in this case:
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 radio On again.