Assuming the remote doesn't have a microphone button (i.e., it's not a voice remote), then it's safe to assume it's an IR remote. You can check whether an IR remote is transmitting anything by pointing it at a digital camera like the one in your phone. Press buttons on the remote and you should see flashes of light on the camera's screen. If not and you've tried new batteries, about all that's left is to replace the remote. If it is transmitting, try standing really close to the TV to see if you get any response out of the TV. The IR receiver is generally close to the light on the TV, but it could probably be anywhere.
One additional thing to check. The remote will only operate if the batteries are installed in the correct direction. Inside the battery compartment there should be a diagram showing you their correct position.
