Any codes, preferably using a dealer-level/fancy scan tool?

Have you checked the inertia switch. You may only have to push the reset button. Refer to your owners manual for details.  

I assume you've tried replacing the fuel pump relay but that didn't work.

You're jumping around with your diagnostics a little bit but you have established that your Fuel Pump will run if provided power.

All of your questions can be answered by testing the Fuel Pump relay sockets.

Let's look at the fuel pump circuit.

I've color coded it to make it easier to discuss.

I'm going to refer to the pins on the fuel pump relay as they're designated in the diagram. (I don't believe they have the pin assignments right but I'll address that later).

So let's look at the "Load Side" of the circuit. (RED)

From what you've posted it seems that you've already tested that Power is going to the Pin 1 socket of the relay.

Your next step should be to jump relay socket terminals 1 & 5. The Fuel Pump should run.

If the pump doesn't run there's a problem with the wiring between relay socket 5 and the fuel pump.

If it does run then it tells you that the wiring going from Socket 5 to the Fuel Pump is good. That the "Load Side" of the circuit is fine and you can troubleshoot the "Control Side". (Purple and Green).

The Power (Purple) to the Control Side of the Fuel Pump Relay (relay's coil) comes through the 30A ECU fuse to the Main Relay.

When the Main Relay is energized (by the PCM) Power continues through the 15A Injector fuse to the coil in the Fuel Pump Relay.

The PCM controls the Fuel Pump Relay by providing Ground (Green) which energizes the Fuel Pump Relay's coil and closes the internal Load Side switch and completes the circuit (Red) to power the fuel pump.

So what can you do with this long-winded explanation?

Here's the drill:

1) Test for Power at Fuel Pump Relay Socket 1 (I think you've done this already).

2) Jump Fuel Pump Relay sockets 1 & 5 (RED) ((the fuel pump should run))

3) "Key On" (to energize the Main Relay) Test for 12 volts at Fuel Pump Relay socket 4. (Purple)

4) While Cranking the starter, check for Ground at Fuel Pump relay socket 2 (Green).

When you figure out which of those 4 Fuel Pump relay sockets aren't getting what they need you can investigate that leg of the circuit.

The Power sides will be easy. The wiring diagram points you to potential problem areas. (fuses, relays, wiring).

If it's the Ground being provided by the PCM (Green) then that's going to be more challenging.

Because now we're talking about issues which @rth3rth3 and @mmj brought up. (Inertia switch, anti-theft, wiring) 

So, it's time to address why I don't trust the Fuel Pump Relay socket numbers the way they're shown in the diagram.

(This isn't unusual with these wiring diagrams. They get wire colors and relay pinouts wrong all the time).

At the risk of boring everybody to death I'll present my case.

Us older guys are used to seeing relay pins/sockets labeled as 30, 85, 86, 87 (and 87A on 5 pin relays).

The Load Side is always Pins 30 & 87.

The control side is always Pins 85 & 86.

Foreign cars use relay pins/sockets labeled 1, 2, 3, 4, (and 5 on five pin relays)

Let's look at your Fuel Pump Relay.

It's a 4 pin relay and it's showing the Load Side as Pins 3 & 5 

and the Control Side as Pins 1 & 2.

That doesn't match the wiring diagram.

The wiring diagram shows Pins 1 & 5 as the Load Side but the relay map shows Pins 3 & 5.

The wiring diagram shows Pins 2 & 4 as the  Control Side but the relay map shows Pins 1 & 2.

That doesn't really matter. Just look at your relay and use the map to apply it to the wiring diagram.

If it doesn't have a map then here's the setup (complete with the "old guy" translation):

Use a test light and let us know what you find out

Could be a wiring fault