If a brown power instructs you to "roll all dice not in birdfeeder," but all dice are currently in the birdfeeder, there are no dice outside the birdfeeder to roll. Therefore, you do not roll any dice, and the rest of the power cannot be resolved unless it specifies an alternative.

This is supported by the description of the birdfeeder management on page 7:

• "The dice removed from the birdfeeder when a player gained food will remain outside the tray until the birdfeeder is refilled."
• Brown powers such as the one on Broad-Winged Hawk (page 1, page 4): "WHEN ACTIVATED: Roll all dice not in birdfeeder. If any are [rat], cache 1 [rat] from the supply on this bird."

If there are no dice outside the birdfeeder, there are no dice to roll, so the effect cannot proceed.

Source: pages 1, 4, and 7.

Source: Core Rulebook (pp. 1, 10, 4, 7, 8)