OK, I have zero Epic mechanical experience, but I run a Toyota specialty shop. On a Toyota or Lexus the fuel pump relay is called the "circuit opening relay" it's a dual coil relay that gets two signals, one from the start switch on teh key that turns the fuel pump on and one that is energized by the ecu that tells the relay to stay engaged because the engine is running. Sounds like the ECU isn't telling the circuit opening relay that the engine is running.
1. locate the fuel pump relay.
2. feel it whole someone turns the key to the start position, you should feel it click.
3. after the engine starts you may feel it "un-click" as the relay turns off.
Looks like this may be a better guide than me....
http://www.epicmarine.com/docs/Fuel_System_Guide.pdfAll of this assumes your engine is dying because of a lack of fuel or fuel pressure.
Aaron