Joe,
I purchased a running 1990 XJ-S convertible (5.3L V12) for my wife in 2005 with 62K miles on it and it now has almost 130K miles on it. I have done most of the work on it over the past 13 years. Except for when I was work on it this car has never sat for any extended period as far as I know. So I haven’t faced what youare facing.
As far as where to start, I recommend that you first get a good library of the technical documents that you need for your car. In the long run this will save you a lot of time, minimize frustration, and save you money on parts.
Here are the documents that I find very helpful for my wife’s car:
-Owner’s Handbook
-XJ-S Repair Operations Manual
-XJ-S Parts Catalogue RTC9900CA
-S57 Electrical Guide
-Kirby Palm’s “Experience in a Book”
Fortunately for me the Owner’s Handbook came with the car. I purchased the ROM, Parts Catalogue and S57 on eBay. You can download Kirby Palm’s book for free from Jag-Lovers. I much prefer the hard copy versions of these documents. I believe that they might also be available in digital format but I don’t have experience with that.
At this point on a car that has sat for so long you could have any number of issues. If I were you I would drain the fuel tank and surge tank to inspect for rust and debris and change out the fuel filter. I would also drain and replace all engine bay fluids, belts and hoses. I would remove and replace the spark plugs and wires and perform a compression check to make sure that you don’t have a dropped valve seat.
Your engine will run if it has compression, fuel, and spark in the correct amount and at the correct time.
Although I have not had experienced the exact problem that you have, I have had failures of coils, crankshaft position sensors, fuel injectors, various sensors, and wiring.
BTW, read up on the “Marelli meltdown” failures of this digital ignition system in both Kirby’s book and in the online archives. It is certainly something for you to be aware of.
Good luck.
Paul