Lincoln LS won't start after back probing fan check all fues and relays,fuel,spark,all ok spray with starting fluid car runs but cut off

did you verify that you have fuel in the cylinders, try a small spray of starting fluid.

need to ck power to jet pump in tank

check the impact switch, the button should be down, if that's good check fuse and relay, if ok replace fuel pump

make sure you have fire at the coil if not there will be no fire to the plugs

Spray starting fluid into the air intake of the engine, if it starts and you have fuel pressure you have no injection or injector pulse as we call it. Check ECM fuse one and two for continuity if it starts with fluid..

check fuel pressure, should be 40 psi.
try 2 things

spray starting fluid in air intake to see if it will stay running. It's fue then.

Try turning key to on nd wait 5 seconds for system to build pressure and pump to shut off. Turn key off, wait for relay clcik noise or 10 seconds. then turn key to ON again and wait 5 seconds to build pressure again. Then start engine. If it starts better, you have a bad check valve in the fuel pump or a bad pressure regulator on the fuel rail (unlikely).

report back

The electric fuel pump is controlled by a relay in the fusebox.
It normally only goes on for a few seconds, and then if the alternator does not signal the engine is running, the relay is supposed to shut the pump off. But you can shunt the secondary wires of the relay to keep it on if you want to check fuel pressure.

Try some starting fluid spray to make sure the ignition is good.
It will at least sputter on the spray, if there is spark.

Here is a picture of an Aztek fuel pump relay:

http://cgi.ebay.com/ebaymotors/Standard-Motor-Products-RY484-Fuel-Pump-Relay-_W0QQcmdZViewItemQQfitsZMakeQ3aPontiacQ7cModelQ3aAztekQQhashZitem45f786818dQQitemZ300505530765QQptZMotorsQ5fCarQ5fTruckQ5fPartsQ5fAccessories

How did you test the fuel pump?
Which one Distribution Pump or Transfer Pump?
Do you have fuel presuure at the rail?
Do you have a crank signal or spark?

V8--V6!

replace fuel filter and (clean or replace) air filter. then pressure test fuel system.

check the fuel filter or the air filter they may be clogged and check fuel pressure