Can we put all the facts together? I can't do well with all of the tidbits all over the place.

It sounds like:
- When you turn the key, nothing happens
- If you leave the key in the "on" position for a while (at least a minute), the car will just start itself without you putting the key in the start position
- The car just shut off last night when idling, even though the key was in the "on" position and engine running

BTW what year is the car?