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If such a device does not power On, the first question after trying a proper replacement battery is, how old is the device? if within a year of purchase date, its failure is covered by warranty.
If not covered by warranty it can still be repaired, but at cost to you, of course.
If you wish to have it repaired, whether covered by warranty or not, let me know your local zip code, please. Or your town/city and state. And I will give you information and the standard price quote, etc.
One thing to try first, either way:
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.