Some time in the early Fourth Era, when the Third Empire had dissolved and all Tamriel was in chaos, Titus Mede captured the city with a mere 1000 men and crowned himself the first Emperor of a new dynasty.
In 4E 174, in the height of the Great War between the Aldmeri Dominion and the Empire, Thalmor troops burned the city in the infamous Sacking of the Imperial City. The Imperial Palace was burned, the White-Gold Tower was looted, and all manners of atrocities were carried out on the innocent populace by the vengeful Thalmor army.
So I think the Imperial city was clearly heavily damaged but how much. Is the White-Gold Tower still standing?