Will not crank over?

For the third time in a month, my 2003 Honda Element has failed to start. This morning, I had to swap cars in my driveway, so I moved out my other car, backed the Element out, and put the other car back. When I got back in the Element, it wouldn't do anything.

No lights come on inside the car at all (no dash lights, dome lights, etc.) No sound is made when I open the door with the key in the ignition. The brake lights, flashers, and horn all work. When I turn the key, there are no sounds made whatsoever and the engine doesn't even attempt to start.

This has happened two other times. The first time, I replaced the battery, to no avail, but after a few hours, the car started. The second time, it failed next door to a dealer, so they pushed it into their garage. They found nothing wrong, but suddenly it started just fine. I took it to a Honda dealer, who said there were no errors in the event log, no blown fuses, and they couldn't find anything wrong with it.

The only other thing I can say is that today, when it failed, the dials on the dashboard had not gone back to 0. Even though the car wasn't started, the RPM dial still showed that it was at 1000 RPM. Also, the gas gauge was down to show 1/4 tank, as opposed to going all the way to empty like it normally does when you turn off the car.

Any ideas here? I don't want to keep paying diagnostic fees to just have the dealers tell me that everything is fine.