When you unlock the doors with the key fob, the computer starts. So by the time that you sit in the car and turn the key, its already on and booted up.

(splash screen only turns on when the computer is starting up)...

An easy way to see the splash screen is to leave the car unlocked for a period of time (so that the computer shuts off - I think its 30 mins). Opening the door has no effect on the computer's bootup, so by the time you sit in the car and turn the key, this time computer will have to boot from scratch, thus allowing you to see your splash screen...