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Did you leave it uncharged for an extended period? It's possible the battery dropped below whatever safety voltage level is necessary before the Kobo will allow a charge.(sometimes this limiting is done by an internal chip in the lithium battery pack) You could use a multimeter set for DC voltage to check the output of the battery. If it's been uncharged long enough, it could have dropped considerably.
While I don't really recommend it, you might attempt recovering the battery by slowly charging it to a voltage in excess of the safety voltage. You have to be extremely careful to monitor the process and it would be best attempted with an intelligent power supply capable of maintaining a current limit with an adjustable voltage limit in a safe location because lithium batteries can be explosive, catch fire, etc. Wear safety glasses, etc., the whole nine yards.
The advice you were given regarding replacing it is probably for the best. If you attempt any of the above you need to be extremely careful to protect yourself and your environment.
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