|If the battery is completely dead it may take awhile before it even gets a minimal charge so keep it on the charger for several hours before you decide you have a problem.|
If that doesn't fix it:
The charger you're using plugs into a wall socket and has a removable USB cable? Check the camera manual but I'm pretty sure the camera is designed to be charged through a USB port on a computer as well. You can try that and if it charges OK then the charger must be bad.
You say you tried removing the battery and replacing it. I don't mean to be dense but using the word 'tried' is confusing. Does that mean you replaced the battery and had the same problem or you tried to replace it but for some reason you couldn't?
If the above doesn't help then since you've only had it a few weeks it should be under warranty.