My Kobo Aura is not recharging. The charging unit seems "dead". Can the charger be replaced?

Through your computer Ter connect the tablet with charger cable go to kobo website put user and password all your will be on account then transfer back over to your tablet

No, Kobo's are not designed to have replaceable batteries.

If the tablet works while plugged-in to the charger, yet dies immediately when the charger is disconnected, it means that the rechargeable battery in the tablet is dead.
If the unit will not turn on at all, even with the charger attached, the charger itself may have failed, or the unit may be having other issues.

No menu required. Just use two fingers on the screen and slide them apart. Be careful, it's easy to get very big, very quickly.
To get smaller slide two fingers together on the screen.

Unfortunately, the batteries on Kobo were not designed to be replaced. If the batteries will no longer accept a charge, it is time for a new e-reader.

Move the on/off slider to the right and hold it there for at least 10 seconds before releasing it will turn the Kobo off. Any less than that and it goes to sleep.

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCcQFjAB&url=http%3A%2F%2Fwww.kobo.com%2Fhelp%2Fkoboarc7&ei=nrvaU6WGKIi1yATyrYHgBQ&usg=AFQjCNFG7S-Ds9hLzf1OyLeqJUIiYg7sQw&sig2=JneUmogw1vf6j2agW-Nf1w&bvm=bv.72185853,d.aWw

hope this helps you ;)

Lithium ION batteries are usually rechargeable. The use mode for these batteries is that there are a set number of recharges that equate to the life of the battery. Usually that life is approximately 1,000 charges.
If you use your battery to 50% then recharge, you can do this ~2,000 times. As the life of the battery is used up, the maximum charge lessens which means where you may have had 8 hours of play time when the battery was new, you will only have 6 hours as the battery life is used up.
In order for a Lithium ION battery to recharge there must be at least a small amount of charge left as a "seed" for that recharge. If you drain a L-ION battery down to zero, it may never recharge again or the max charge will be reduced to an insignificant amount of the original full charge. eg instead of 8 hours you may only get 15 minutes, or 5 minutes, or no minutes.
You are much better off recharging when 50% depleted than using it up til your product stops.
L-ION batteries cannot be repaired only replaced. Most cheap products using L-ION batteries cannot have their batteries replaced.

Probably, the ac charger unit isn't good anymore. Output charge voltage& current isn't sufficient to drive your battery charge beyond 80% threshold.

Change or replace this with a new one (same ac charger specs please) and charge your tab again.