Two things. Turbo timers are pointless on any WRX.
And, it's your fuel pump or something related to it. I can't explain the correlation between stalling and you not starting again though.
But if you turn the car to "on" and you don't hear the whine of the fuel pump something's wrong, and that should be the first place you look.
You need the engine to crank, sparks from the plugs, and fuel to start the car. You're battery's not dead, you said it's sparking fine so your plugs and more importantly your distributer's fine, so that leaves fuel. And you said you don't hear the fuel pump when you put the car to "on". So... Since the car started eventually it's not a fuse blowing.
And since the car eventually started and ran fine it's probably n ot the fuel pump itself but something that controls the fuel pump.
I'm just rambling about what's going through my head so.. I dunno.
Did you get the car started yet? Just keep cranking it. I had a similar problem and it took FOREVER to get fuel back into the engine and then i tstarted.