This sounds like an issue with low fuel pressure. It can be the result of a faulty pump or a partially plugged filter. The first thing I would suggest is to check pressure. Here is a link that explains how it is done. You will need a fuel pressure gauge to test, but most parts stores will lend one to you.
Here are the directions specific to your vehicle. The attached pics correlate with the directions. The pics are diagnostic flow charts for issues that are found.
If you look at the attached pic, it shows the manufacturer's specs related to fuel pressure requirements. I highlighted your vehicle.
If you find the pressure is low, I would start by replacing the fuel filter which is mounted on the passenger side inner fender under the hood. Here are directions for lines and fuel filter replacement. The attached pics correlate with the directions.
2004 Lincoln LS V6-3.0L DOHC VIN S
Vehicle Powertrain Management Fuel Delivery and Air Induction Fuel Filter Service and Repair Procedures
FUEL LINES AND FUEL FILTER
Disconnect Tool, Spring Lock Coupling
- Do not smoke or carry lighted tobacco or open flame of any type when working on or near any fuel-related component. Highly flammable mixtures are always present and may be ignited, resulting in possible personal injury.
- Fuel in the fuel system remains under high pressure even when the engine is not running. Before repairing or disconnecting any of the fuel system components, the fuel system pressure must be relieved to prevent accidental spraying of fuel, causing personal injury or a fire hazard.
1. With the vehicle in NEUTRAL, position it on a hoist.
2. Disconnect the battery ground cable.
3. Relieve the fuel system pressure.
4. Remove the left front wheel well rear splash shield.
5. To remove individual components, only carry out the listed steps.
6. Illustration 1 of 4. Remove the components in the order indicated in the illustration and table.
7. Illustration 2 of 4. Remove the components in the order indicated in the illustration and table.
8. Illustration 3 of 4. Remove the components in the order indicated in the illustration and table.
9. Illustration 4 of 4. Remove the components in the order indicated in the illustration and table.
Item 2: Spring Lock Coupling Removal Note
1. Install the special tool.
2. Press the special tool into the open end of the cage.
3. Separate the spring lock coupling.
1. To install, reverse the removal procedure.
If pressure isn't restored after filter replacement, then you need to suspect the pump is bad.
Here are a couple links you may fine helpful:
I hope something here is helpful. Let me know if you have other questions or need help.
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Friday, April 17th, 2020 AT 8:13 PM