If there is no red light either the light itself could be damaged, the battery could be not charging or the charger could be not working. I would try seeing if it actually charging first. If it is, then I wouldn't worry about it. If it isn't charging, then I would try a different charger. If it is charging but seems to not be holding a charge long, then it is probably the battery.
NOTE: If the device is under warranty, then contact the manufacturer about the issue.