So Popper is wrong: his theory was not falsified. When the remote continued not to work, he could have rejected his theory about the dead batteries, but he could just as easily have rejected any of his other assumptions about the world. As Quine said, our beliefs about the world can only be tested against the world as a group, not individually, and this holds for falsification just as much as for verification. No theory, in isolation, is falsifiable.
This is incorrect. The theory "my tv didn't turn on because the batteries are dead" is falsified/can be falsified by changing the batteries. The theory "my batteries are dead" can be falsified by using the same batteries in a different device. These are different claims with different falsification tests, which have been conflated here. Popper is not refuted.