The FI on these engines runs off the Alternator -- not the battery (that's what all those relays do). Your fuel pump will shut down after starting if your alt isn't putting out enough current (Amps!!! A Voltage check done by your local autosupply store won't tell you this.)

In other words, the dash lights will come on (like normal) as you turn the key on, your engine will start when you move the ign to that position, the dash lights will stay on even after the engine is running, then the engine will die.

Do a search for "dash lights" or "alternator" and read all the posts. You may be surprised.