apple tv model 1469 flashing white light

If a power cycle doesn’t resolve it, then Restore your Apple TV through iTunes - Apple Support

The rapidly continuing flashing status light would indicate a failure to start up properly. This can often be corrected by reinstalling the software through iTunes on a computer.

Re-connect to the TV it worked on and then do a Reset and then plug it into the new TV and you will have to re-set it up.