You may want to check the new battery. Also name brands tend to work better. Do a bit of searching on this forum and you will find quite a few posts regarding the fob battery.
If you have a multimeter, check the voltage of the CR2032 battery. It should be between 3.2-3.4 VDC. If it's 3.0 VDC or lower, it's about done.I was getting the warning that my key fob battery was low so I replaced it. Since then, it's like the fob needs to be reassociated with the car. I can only start the car using the process I found on this forum. Otherwise, I get an error on the dash saying something like key not identified. I've tried multiple times to no avail to pair the key. Any ideas?