The remote part of the key may have failed, but it may just have gone out of sync due to a battery inside it going low.
Even though you have replaced the internal battery - it may still need re-syncing with your vehicle.
You can try this - using the instructions below. In the instructions - it will be referred to as - 'Alarm Remote Manual Programming' to the vehicle.
Try the below instructions - and if you are not successful with this key - then the remote side of this key may have completely failed. This can be replaced separately from the key blade.
Alarm Remote Manual Programming X-Type
• The ignition must be cycled four times between Run and Accessory four times. It is important to end the cycle in the Accessory position.
• This starts the programming mode, which is indicated by a chime from the GEM.
• The key must be removed from the ignition. Following this, press a button on the RF transmitter within 10 seconds. If the RF transmitter has been accepted, the GEM emits a chime.
• To program further transmitters, press a button on the next RF transmitter within 10 seconds of the previous entry.
• Up to 4 RF transmitters can be programmed into the GEM.
• The programming mode can be terminated when any of the following occurs:
o The ignition is switched to Run,
o No further RF transmitters are programmed within 10 seconds,
o An attempt is made to program more than 4 transmitters.
• Once the GEM has dropped out of the transmitter-programming mode, restarting the process will and programming another RF transmitter will erase all previous transmitters that were stored within the GEM.
When carrying out the above process, please ensure that no other vehicles within a 50- meter radius are undergoing the same programming procedure; this could affect the programming operation.
I hope this resolves your concern.