I have a 2004 WRX, no performance mods/110k miles/automatic trans.
I do, however, have an automatic starter.
This problem started out of the blue about a 2 years ago, I would try to use my keyless ignition and the headlights would turn on, car would try to start, then couldn't. It does not happen all the time, and I've yet to pinpoint when it will happen/won't.
After dealing with my car alarm/autostart installers, we replaced the unit, but the problem persisted.
The only fix is, I can put my key in a turn it forward, with foot on brake, put the car in neutral (this is sometimes difficult), then once car is in neutral, I can start the car. This solves the problem every time.
It seems like my car doesn't realize it's in park or something.