2000 Jaguar S-type 4.0 sport no fuel pressure at fuel rail new fuel filter, fuse is not blown, and can't find a fuel pump relay anywhere. Cranks over well, should my next step be to replace the fuel pump itself?

First check there is battery voltage to the pump and the pump starts when the ignition is switched on , if not check fuse and relay, check wiring from relay to pump. If ok and the pump is working , check for fuel blockage from the tank inlet to the pump , some have a sock type filter in the tank pick up tube, if all ok remove the fuel filter , switch on and fuel should flow at the filter, fit a new filter, if still no fuel at the rail fit a fuel pressure gauge an check for low pressure , if ok, the fuel pressure regulator may be stuck causing a air lock replace it.

Bad fuel pump or relay to fuel pump or blown fuse to Main Relay or bad relay, could cause no spray from injectors.
Hope this helps.

The first thing i would check would be the fuel pressure, the gas being sold now a days eats away at the fuel pump and makes varnish build up in pump causing the pump to go bad.

A fuel pressure gauge is needed for this test, it connects to the fuel rail and give you a reading and i would bet there is no or very very low pressure.

The engine for the Jaguar S-Type is the same engine as the Land Rover RR Sport, and the U3E22 code is misfiring due to low fuel pressure. Low fuel pressure could be caused by a number of things, which you already suspect:
fuel pump, leaking fuel injector, leak in fuel rail, clogged fuel filter or clogged in-tank fuel strainer, possibly even a leaky/kinked fuel line, or fitting/banjo bolt.

check if the input side of the fuel pump has a restriction . a perished rubber hose can be a problem , the pump should be able reach a pressure 35 psi + and a flow of a quart every 30 seconds at this pressure.

RESET THE COMPUTER, IT WORKED ON MY XJ. SAME PROBLEM I HAD.

1) jack-up left front of car (drivers-side)and remove wheel.
2) Remove plastic inner fender .
The maintenance schedule is every 12-thousand miles.

Caution prior to removing fuel filter-
Pull the fuel pump relay or fuse while engine is running, this will disable the electric fuel pump and release fuel pressure in line.

Air - not likely the problem ! mechanical cable controlled throttle body

Fuel- make sure there is gas in tank! fuel pressure test at the throttle body or rails, if no fuel check power to fuel pump: ignition power to breaker or fuse, relay , power to pump at 3 pin connector near tank/frame rail on drivers side, - if pump is runniig but insufficient pressure, check for mechanical restriction: plugged filter broken or pinched line, plugged pickup tube in tank. if good pressure to rail or body, check ecm : diagnostic codes, fused power, ecm tells injectors when to open, dependent upon several sensor parameter inputs.

Spark- ignition - coil-distributor-ignition module (or coil packs)- wires-plugs-ignition module (signals coil to discharge, mounted beneath distr cap) work backwards from plugs.

This may be a fuel problem. You will need to gain access to the fuel pump relay or fuel pump to confirm that voltage is available to the pump when the key is in the run position. A simplier way to verify fuel is to hook a fuel pressure gauge to the shrader valve on the fuel rail if one is available.

fuel pump relay