You may not think so, but it sounds like you are making progress. With the judicious use of starting fluid (aka Mechanic-In-A-Can), you seem to have narrowed down the fault to an ignition problem.

One important warning: Be EXTREMELY cautious with starting fluid. If you get no response from a quick burst (3 seconds max), stop and investigate why. Don't just keep repeating the spray and pray routine, hoping the engine will fire off. The lack of response indicates the plugs are not firing for reasons unknown. More starting fluid isn't going to fix anything, and has the massive potential to cause major damage. /[Soapbox mode off]

Moving right along, given the chance to spend your time and money, here's how I'd proceed.

1) Move to a warmer climate. It's no fun working in booger-freezing cold.

2) Charge that poor battery, and keep it fully charged during all troubleshooting. This is a very important step, so please don't skip it.

3) Read step #2 above one more time.

4) Read step #3 above one more time.

5) Scroll up to post #2 near the beginning of this thread. Make sure the indicator light for the security system is operating normally.

The preceding are basic prerequisites for troubleshooting. Now on to actual isolation of the fault:

6) Take a look at the wiring diagrams for your car, near the top of this page:

JagRepair.com - Jaguar Repair Information Resource

See figure 03.3 for the V8 ignition system. Notice how all 8 coils receive power from a common source. Follow the 88P inside a circle to figure 01.6 for the upstream portion of the ignition circuit.

7) From figure 01.6, check fuse F12 under the hood.

8) If the fuse is good, reinstall it. Turn the key to Run (not Start) and measure voltage at both side of this fuse. You should be able to fit the tip of a voltmeter's red probe into the little test slots on top of the fuse. Use a paper clip or similar as an extension if needed. Connect the black probe to a good ground. Make sure you have battery power present at both sides of the fuse.

There are more steps we can do, but try these steps to begin the process. Keep us posted.

 

All those bits of information that we are slowly dragging out of you do help!

Now you mentioned something disturbing? The car has been sitting for long periods of time. Two things from this?
First is there ANY chance that rodents/mice have chewed on a wire harness somewhere? This is way more common than you might think.
Second even though you now appear to have a electrical problem and the plugs are not firing we have seen many fuel pumps seize up from sitting. So when you get it back running be aware you "might" need to replace the in-tank fuel pump too.

Follow Karl's advice and report back. I do think your getting close!
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Did you manage to solve the problem? I have the same problem with my 2004 2.5L V6. The car stood for 4 years but did start at once when I bought it, not now in front of my garage. Fuel pressure is OK, no spark, no fault codes except Hand Brake.

 

. . . and another one bites the dust! This is not meant to offend . . . just that your issue has been a recurring theme for at least a decade on this forum, so some reading is called for. That said, we are here to help, so here is the often repeated solution . . .

The clue to your issue lies in the EPB (Hand Brake) warning, and this is one of a succession that can include cruise control, transmission etc. Put simply, even if there is enough battery charge to start the car, these warnings indicate there is insufficient to correctly run the many peripheral control modules around the car. Your car doesn't have even enough battery charge to start the car, let alone the electronics.

Suggest you read up on the S-Type's notorious need for a fully charged battery that needs at least 12.7 volts standing charge . . . ie at least 12hrs after a full charge. Start with the Stickies atop this forum. Go to "How to . ." > Miscellaneous > Battery 101. You will find that even brand-spanking-new batteries come from the shop with less than this 12.7volts. If you have a DVOM (multimeter), measure it. If you don't, a simple no-nonsense one can cost about $10. A battery charger that cuts out when reporting "charged" is no substitute. Especially for a seldom used S-Type, a permanently connected smart charger is, IMHO, a mandatory investment . . . and far kinder than occasional starting and idling.

If, as I suspect, this solves your issue then . . . please . . . a simple request. Unlike this thread's OP who vanished a year ago with no update, please let us know the result. If not, I suggest you begin a new thread stating issues and progress. Jumping on a year old thread often fails to inspire the help you seek.

Cheers,

 

Thanks but it didn't work. I'm going to start a new thread.