Brake pedal is almost impossible to press in

Welcome to 2CarPros.

It sounds like you lost power assist. The brakes on this car are assisted by engine vacuum. So either the vacuum supply is lost or the brake booster is bad. If the engine is still running smoothly, then I suspect the booster is bad because a large vacuum leak will cause the engine to stall or run really rough.

Here are the directions for replacing the booster. Before just replacing it, confirm there are no vacuum leaks and check the one way valve to see if it is bad. Basically, it will allow vacuum to go one way and not the other.

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2004 Jaguar S-Type (X200) V8-4.2L
Power Brake Actuation Booster
Vehicle Brakes and Traction Control Power Brake Assist Vacuum Brake Booster Service and Repair Procedures Power Brake Actuation Booster
POWER BRAKE ACTUATION BOOSTER
Brake Booster

Removal
1. Remove the brake master cylinder.

Pic 1

2. Disconnect the brake booster pedal travel sensor and brake booster solenoid electrical connectors.

Pic 2

3. Remove the brake booster retaining nut.

Pic 3

4. NOTE: The non-return valve and vacuum pipe assembly should be removed with the brake booster.

Remove the brake booster retaining nut.

Installation

pic 4

1. NOTE: When renewing the brake booster, the non-return valve and vacuum pipe assembly should be installed prior to the brake booster installation.

NOTE: Replace the brake booster/pedal box gasket.

To install, reverse the removal procedure.
Tighten to 25 Nm.

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Let me know if this helps.

Take care,
Joe