If the light on the key fob does not light up, that usually means that there is insufficient voltage in the battery.
When you changed the battery, did you put in a known make from fresh stock? Some of the cheaper brands from ebay, pound shops and the like are very dubious quality! Some even show the correct voltage when 'resting' but when under even a light load drop massively.
It may be worth trying a good (more expensive!) battery.
The symptoms you describe sound like a duff battery.
Also, clean the contacts in the fob before you replace.