Confusingly, there is a 2012/2013 3rd generation model, and there are 2022 4K 3rd generation models.
Identify your Apple TV model - Apple Support
Find your Apple TV model number - Apple Support
It seems that Conference Room Display may be currently active, showing screen saver images. You should be able to exit that by using the Menu or Back button. Conference Room Display could be locked with a restrictions PIN number. Conference Room Display could be locked through a device profile (enterprise use).
Conference Room Display can normally be turned off or on in Settings﹥AirPlay﹥…
For legacy models: Use Conference Room Display mode and related settings on your Apple TV - Apple Support
For current models: Using the Conference Room Display feature - Apple Support
Remote seems to connected to Apple TV as light blinks when press button
It is a bit more nuanced. Apple TV may acknowledge receiving a remote signal even if that remote is not paired or linked; Signals from unpaired or unlinked remotes will be ignored though. It only tells you that the remote is sending something (i.e. the battery works).
To pair or link again, if the connection got lost somehow, do as described:
For legacy models (linking): If your Apple Remote (aluminum) isn’t working - Apple Support
For current models (pairing): Pair the Siri Remote with Apple TV - Apple Support