Arnon

Blue box: "You will not solve this puzzle."

White box: "Four statements on boxes in this room are true. A box with one false statement contains gems."

Black box: "A box with a true statement contains the gems. This box does not contain the gems."

A: White

I've tried blue and white as I had two wind-up keys.

Blue: "The gems are in a box with the longest word. 'Longest' is the longest word on a box.

White: "The gems are in a box with the shortest word. 'A' is the shortest word on a box.

Black: There are words on the box with the gems. This box does not contain the gems."

A: Blue