How can fix this problem

Does not look good. The fact the charger light won't change colour, could mean the battery can't get enough charge. The voltage stays too low. Check if the battery is put in correct in the camera.Check if the battery contacts are clean and shiny. also check the contacts in the camera. If you need to clean the contacts, don't use anything sharp. just a dry cloth or cotton swabs. Sharp tools will damage the camera and or the battery. If you have an external (universal) charger, try to charge the battery outside the camera.
I did write lots of things about batteries, because they are the most common reason for camera malfunction.