First, you did not say how old the battery is. Rechargeable batteries do not last forever and if left on the shelf for prolonged periods can discharge to the point that the suffer permanent damage and will not take or hold a charge. Most rechargeables last for about three years give or take. It could be that your battery simply needs replacement. You identified your camera as a Coolpix 3200, I presume you mean an S3200.
Start by removing the battery from your camera and making sure that the battery contacts in the camera and on the battery is clean. Dirt and grease can prevent the charging current from flowing to your batteries. If they are dirty. A new pencil eraser can be rubbed against the contacts both in the camera and on the batteries to remove any oils or residue. Next, I would try to charge the battery again.
If that does not work, replace the battery. Your camera takes a model EN-EL19. Since new batteries normally have a partial charge on them, I would first see if the camera will power up and take a picture. If so, the next step is to see If the new battery will charge in your camera. If it does, you have solved your problem. If not, the camera's charging circuit may be at fault. If that is the case, you have two choices. You can send the camera Nikon USA for repair or, if the camera otherwise functions correctly, you can save the cost of repair by purchasing a model MH-66 external battery charger and charging your battery outside the camera.
If you need to send your camera in for repair, you can call Nikon USA Service at 1-800-645-6687 9AM-8PM EST, Monday to Friday for assistance or go to there website (link below). They will give you a free repair estimate if your camera is out of warranty.
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