Alternatively put: has an aircraft carrier ever been sunk by cannon fire alone?
As I understand it, the coming of the aircraft carrier in WWII pretty much put an end to battles where ships saw each other, I'm wondering if a surface ship ever got close enough to hit a carrier with its main armament to sink it.
Yes. Take a look at wikipedia's list of sunk aircraft carriers (I don't know who makes these lists, but they are awesome). The only ship that matches your strict criteria seems to be the HMS Glorious, as the Japanese Chiyoda was first damaged by US aircraft before being sunk by US surface ships.
The HMS Glorious and her two supporting destroyers were sunk in June 1940 by two German battleships, the Gneisenau and the Scharnhorst. Only 40 men were saved and over 1500 lost. The incident was quite an embarrassment to the Royal Navy, not only had multiple ships been lost to a smaller force, but they only found out about it when the Germans boasted about the encounter on the radio. The HMS Glorious had been unable to raise any other ships to inform them of its plight.
You can read more about the sinking of the HMS Glorious in Howland's The Loss of HMS Glorious and in John Winton's Carrier Glorious.
I think that happened during the great marine turkey shoot