The Great WarEdit
During the middle stages of the Great War, Alpha Squadron under Duke's command was deployed to Char to retrieve Sarah Kerrigan, who had been abducted by the zerg. The Norad III was Duke's flagship during the battle. However, the zerg attacked and defeated the terran fleet, and things weren't made easier when the Protoss Expeditionary Fleet arrived and destroyed most of the terran ships.
Though Duke's fleet suffered great losses during its attacks on Char, the Norad III managed to escape.
After the Great War, Norad III led Alpha Squadron to Bhekar Ro, a backwater colony world which had then discovered a xel'naga temple. The Squadron's fleet was destroyed or disabled fighting the protoss and zerg attempting to secure the temple, and temporarily stranding the survivors. Norad III was subsequently repaired and returned to service.
The Brood WarEdit
The Dylarian ShipyardsEdit
General Edmund Duke led the Dominion Armada to the Dylarian Shipyards from the Norad III in a reprisal against the UED Expeditionary Fleet which had commandeered a number of battlecruisers in dry-dock. The Dominion fleet was repelled.
Siege of AugustgradEdit
With the fall of Augustgrad to the UED, Emperor Arcturus Mengsk attempted to escape aboard the Norad III but was headed off by the Aleksander. The ship was rescued by Commander Jim Raynor and escaped via dimensional recall along with the Hyperion and a small protoss fleet.
The Last BattleEdit
The Norad III returned to Augustgrad after the liberation of Korhal, but was ambushed by Sarah Kerrigan's forces shortly after the zerg launched a sneak attack on Mengsk's base of operations. The ship was destroyed with Duke aboard.
In Shadow of the Xel'Naga, Norad III was an extensively refitted and renamed Norad II. All of Alpha Squadron's battlecruisers were destroyed during the Battle of Bhekar Ro; if taken to mean the ships were unsalvageable this would preclude Norad III's appearance in StarCraft: Brood War.
Firstborn stated that merely most of Alpha Squadron's ships were destroyed at Bhekar Ro. This allows Norad III to survive either by reflecting subsequent salvage or by retconning Shadow of the Xel'Naga's battlecruiser statement.
North American Aerospace Defense Command (NORAD) is a joint Canadian/United States military organization.