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I would advise you to leave it on the charger for at least 4 hours, continuously and without interruption.
Then try turning it On normally, once more.
- If it fails to turn On, it probably needs a new battery, or else needs to be service-repaired, depending upon its age measured from its date of original purchase.
- If it turns On fine, see whether it stays On for a reasonable interval (a half hour at least.) If it does stay On that long, the battery's fine and it just had a temporary problem.
Let me know, what happens, and how old the Kobo is, please, and I will advise you further as appropriate.