Try rebooting the Chromebook by pressing the Refresh button and the Power button at the same time.
When you plug in the charger you should see a light next to the plug indicating whether it is charging or not.
If you don't see the light check the charger and the plug. Make sure it is plugged into an outlet that works.
The charger is actually two pieces. The charger or ac/dc converter and a cord that plugs into it. Check to make sure the cord has not come loose.
Check the connection where you plug it into the Chromebook. Make sure it is not damaged. If it is damaged it will need to be replaced.