Might be just a coincidence with regards to changing the batteries and the Stick then stopped working.
You can try ploughing through this trouble shooting help guide linked below.
Whilst at it i would be also tempted to try a reboot of your Router before carrying out the trouble shooting instructions.
Replacing the batteries twice in two years is extremely good for the NOW Stick smart remote, where i was replacing batteries every 4 weeks approx on my NOW Smart voice remote controller.
That makes so much sense about plugging it into the TV, thank you 😊 I went through a spell of turning the stick off everytime I turned the TV off, and it didn’t overheat, but it didn’t overheat every day anyway, so I wasn’t sure if it was really making any difference.
I’ve had loads of trouble with routers, so I’ll definitely look into that, thank you 😊
Because there is no light either on or blinking on the Stick then it would normally point to one of the 3 components is at fault ie The Stick itself, the USB cable which could be broken or the supplied power adapter which is not providing power to the Stick.
Once your have eliminated the USB cable by using a replacement cable and trying the USB port if there is one on your television (where newer television should have a USB 900ma or 1A USB port on them if they have more than one USB port) or swapping out the mains plug with a suitable USB 5V DC 1A mains charger plug then the fault lies with the NOW Stick and might need replacing.
When looking at either the Fire Stick or Roku Player product range do you research on them because they are slightly different and may not have all the things that you might be used too using the NOW Stick.