Once plugged in.... the lights are always on. However, look at the oval around the power button. Does it turn off and on when you push that oval switch?
Are you pushing the switch on the box? Or the power button on the remote?
With the TV connected.... does the TV continue to show video when you push the power button?
Your TV box is defective and needs to be replaced, hopefully it's not the bigger PVR box, your recordings will be lost if so.
Occasionally a bad remote can be the cause as well, test your remote on another box in the house if you have more than one.
But if the pushing the power button on the front of the box doesn't work consistently, or after unplugging and plugging in the power cord, the power light should flash for a while as the box boots up.
We also see boxes where all 4 lights on the box are stuck on permanently, this is a defective box indicator as well.