What prevented the Capitol Building from being completely destroyed by arson in 1814?

Two answers:  1) A summer rain and 2) forward thinking building materials that made a large portion fireproof.

The Capitol was still under construction when it was set ablaze with gunpowder paste by the British.  The north and south wings were completed and in use, but construction on the center building had not even begun.  This area was spanned by wood.  The north and south wings sustained damage, but many of the interior spaces were well preserved.  That is because the architect, Benjamin Henry Latrobe, had been using sheet iron, marble, sandstone, zinc and copper for the construction.

The British started the blaze by focusing on major interior rooms, piling furniture and books to start the fire.  Much art, literature and furniture was lost due to being used as kindling.  One of the rooms set on fire was the House of Representatives which is now Statuary Hall.  Statuary Hall was the backdrop in many of the current riot videos, where the crowd is bizarrely shown minding the velvet directional ropes.

Image: Statuary Hall with rioters (MSNBC screengrab); Statuary Hall pre-riots (Wikipedia)