It could be a security issue.
A buddy of mine's wife's 2004 Chevy Malibu would not start one afternoon. They had it towed home. When they got it off the truck it started and ran fine.
Turned out that the problem was the lock cylinder in the column. The car's security system looks for a certain resistance from the lock cylinder, and if it doesn't find it, it will not allow the car to start. As the cylinder starts to wear/age, the resistance can change.
In order to get the car to re-synchronize with the cylinder and start you have to leave the key in the ignition in the ON position for 10 minutes. It will work for a while again, and then all of a sudden refuse to start again.
The tow truck driver left the key in the ignition in the ON position for the ride home, which took way more than 10 minutes.
Maybe you have the same problem? Fiddling around with the radio, presumably with the key ON, for about 10 minutes... Right?