With the removal of the dependent "Then", how does Display of Power now work?

Display of Power says: “After you lose an unopposed conflict – cancel the ring effect of that conflict. Then, you resolve that ring effect as if you had won the conflict as the attacking player. Claim that ring.”

“That ring effect” and “that ring” refer to the ring effect that was cancelled (and its associated ring). Therefore, if no ring effect was cancelled, then the ability can do nothing more. Note that once the normal ring effect for the conflict has been cancelled by Display of Power, you can’t play a second Display of Power as it would have nothing to cancel.

[Tyler Parrott, 30 Dec 2019]