Its the 2005, 3.4 liter, base model sedan. Showed my brother the wiring diagram this evening and he pointed out my mistake on the year. (facepalm).
I have had two Impalas with the 3.4. As I recall, your symptoms are much like those of a failing fuel pressure regulator. The car starts, but won't stay running. You can test it by borrowing a fuel pressure gauge from a parts store, and connecting it to the schrader valve at the end of the fuel rail on the passenger end of the motor. With engine off/key on, the fuel pressure should be in the range 52-59 psi. With the engine running at idle (assuming it cranks and fires), it should drop 3-10 psi.
The regulator sits at the end of the fuel path, on the front bank of the motor, driver's end, near the throttle body. You'll need a torx tool to get it out. Not sure that else - it's been too long since I last did one.