http://www.amazon.com/Harbor-unfoug...1-1&keywords=pearl+harbor+the+unfought+battle
The scenario is based off this book^.
What if Kimmel and others found out about Japanese spies at Pearl Harbor and prepared better defenses?
Basically a warned US Navy is going to sortie and 'NOT' blunder blindly around the pacific waiting to be sunk at sea, but with draw to the East within Land based air cover range, Rendezvous with the Carriers while maintaining a land based CAP and await developments.
Meanwhile any attempt at attacking an Alerted Pearl will result in heavy losses
However unless the US do to the Japanese Spies what the British did to the German ones and effectively sucker the Japanese high command into attacking, then word of the fleet will get back to the Japanese strike force and they too would with draw.
Japan and the US are already at war at this point - the message from the Embassy already decoded before the attack but word reaching Pearl too late to impact the readiness of the defenders.
What happens after that???
As for Sinking battleships at sea several points
The POW and Repulse with 4 destroyers were attacked by 88 'Land based' Aircraft and had no air cover of their own.
An alerted US Fleet having sortied would have had at least 8 Battleships, 8 or more Cruisers, 3 Fleet Carriers, 50 Destroyers and a couple of hundred land based fighters (in addition to their own carrier fighters) with which to oppose the Japanese carrier forces attempts to attack them.
Its a lot harder to hit and sink a ship at flank speed, closed up at battle stations with air cover vs one tied up along side with the crew doing anything but being at action stations.
The British Navy discovered in 1940 that even a handful of planes would seriously disrupt a large attack on a fleet.
What would have happened at Pearl by the morning of the 7th had the US had proper prior warning is that the US Fleet would have regrouped east of the Island and the various organisations stood to.
Japanese "Spies" (assuming they had not been turned or replaced in this ATL) would have reported this to Japan and I am absolutely confident Nagumo would bottle it in keeping with the IJN's doctrine of conservation of fleet strength over a now risky attack and return the fleet to Japan.