First of all, let me begin this web with Alan Dershowitz's lawyerly observation:

Why would a media-savvy and clever man like Dick Cheney delay notifying the press and the police about an accident when a) he knew it would eventually be covered by the press and b) he knew he would be criticized for delaying release of the story?
A simple cost/benefit analysis suggests that he (or those advising him) must have believed that there was more to be gained than lost by a 14 hour delay that would eventually be made public. It is likely, therefore, that something happened during that 14 hour period which was worth the negative costs of the delay.

This makes perfect sense to me. Something needed to be hidden...and hiding that something was worth the shit storm over the 14 hour delay. Dershowitz and most others are speculating that it was, more than likely booze.

I have a different take.