If this car has been sitting all summer, I'm betting the timing chain tensioners were never replaced/updated and they broke, the transmission went out or the computer controlled suspension took a dump (not all of the cars have the "CATS" suspension so this isn't always a concern). The depreciation on these cars, like most high end luxury cars, is horrible so it makes these repairs more expensive than to simply replace the car.
Jaguar improved the design of the tensioners, but kept them plastic, in late 2000 I think, and then changed it to a metal part in 2002 (the 4.2L engines). The general consensus is that the updated plastic ones are adequate, but the metal ones are bulletproof. Also, while Nikasil was an issue, if the car hasn't had problems with it yet, it probably won't. The Nikasil coating on the aluminum cylinders (so a steel cylinder liner wasn't needed) would react with sulphur in gasoline and would flake off, exposing the relatively soft aluminum cylinder to the piston rings. The cylinders wouldn't last long after that. Gas in the US has been low sulfur since 2006 and the number of nikasil related engine failures has pretty much dried up since then.
I love my 2001 XJR, but have never driven an XJ8 so I don't know how much of my experience will transfer over. As was mentioned, the suspension is kind of floaty. It's not bad in the XJR, but it has more aggresive suspension tuning than the XJ8. Even with the XJR suspension though, this car is incredibly comfortable for long distance trips. I recently had an 8 hour drive, stopping only for gas and a quick meal and I felt like I could have gone for another 8 hours without getting tired or uncomfortable. My gas mileage on that trip was about 24mpg according to the car's computer. I average about 23mpg overall, with more highway driving than city driving typically. The XJR requires premium because of the supercharger, I don't know if the non-supercharged cars use regular or premium.
The steering is horribly light - I think Jaguar's standard is that the Queen must be able to steer the car using only her left pinky finger and if she realizes that she is steering the car then the steering is still too heavy.
If you need to carry a lot of things in the trunk, make sure it's big enough for you. These cars have full size spares, and the top of the trunk sits relatively low, so the trunks don't hold a lot. The aluminum bodied cars (2003+) have a much larger trunk, and are a much larger car overall, despite weighing a few hundred pounds less.
Other than that, get a pre-purchase inspection. A good Jaguar mechanic should be knowledgeable about the problems with these cars.
If the car is running and in good shape, you won't be disappointed.
Bob