my 93 accord is having a similar situation. When the key is in position 2, the gauges don't light up, but I can use the windows. If I move the key slightly towards start, all the gauges light up. If I start the car and release the key (allowing it to fall back to position 2), the car dies. If I start the car and hold the key so that it doesn't hit position 2, the car stays running.
This seems to happen when it's hot. I can start the car and drive it easily when it's cold (morning or evenings).
I'm going to replace my ignition switch, but is there anyway to avoid having to spend $300 on it? (Dealer won't sell individual parts...they said it comes together in a bundle or something)