Have you tested the power cord to make sure it is actually allowing for a charge? If that isn't the case your options are to have the battery checked (which if under warranty you don't want anyone other than the manufacturer doing) or doing a reset of the device. You have two options. A "Factory Reset" or a "Hard Reset". both are last resort options, as they erase some or all data.
The first, the "Factory Reset", can be done by depressing the pinhole on the device. Just don't use anything sharp! This will erase some data on the tablet, but may resolve your problem.
The second, the "Hard Reset" removes all your data. The instructions on how to do it are as follows.
NOTE: Doing this will clear the data on your tablet, so it is...