Well it definately sounds like a fuel pressure issue.It's just not getting enough gas to the injectors.It's slightly possible it could be an ignition issue also.But I'm going to lean towards a fuel problem.Four things that could cause this.Fuel pump excessively low output,fuel filter excessively clogged,fuel pressure regulator totally failing and diaphragm collapsed plugging fuel flow...or fuel pump relay or more specific the CCRM (Constant Control Relay Module) which houses the fuel pump relay.Fuel pump speeds are adjusted from here.
Replace fuel filter,turn key on several times to prime fuel system afterwards.Attempt to start and run engine.Test throttle response.If you still have the same problem,shut the engine off,now turn key on (but dont start) and listen carefully in the back for fuel pump noise.Put back seat down to hear it better.This is a 1 1/4 second noise.It's your pump turning on then shutting off when it detects no engine rotation.You should be able to hear this.
I would get a fuel pressure gauge from your local auto parts store (make sure you get one that is made for fuel injected engines...NOT carbs).One that connects to the schrader valve on the chrome fuel lines.This valve looks exactly like a tire valve.Once you have this,attach the gauge to the valve and now start the engine.Your pressure should read anywhere from 25psi to 40psi but no less than 25.If it is then you have a fuel pressure problem and most likely a clogged filter or bad pump.
Another possibility is a bad TPS (Throttle Position Sensor).But first get the pressure checked and then go from there.
How many miles on the engine?