I don’t know much about this car and am not familiar with it. My Jaguar experience starts with my 71 E-type up to the 1992 XJS.
It has been at a friends body shop for a few years because the owner has changed his mind on exterior colors and interior material and color, etc. Apparently the car will not start, it turns over, but does not fire up.
It has been at a Jaguar dealership in Cary, NC for 3 months. The dealer suspected the fuel pump. It was replaced, but still no go. I offered to ask you experts of your opinions of where to look next?
The first thing that comes to mind is loss of compression due to “wash down” of the oil in the bores, get them to pull all 8 plugs and squirt a small ammount of engine oil into each cylinder.
If when it is cranked the engine spins over almost silently it is almost certain to be the case. Turning the engine off immediately without getting up to temperature or a cold start stall is usually the cause of this and the early X308s all suffered from it, there was a software upgrade to fix it which may or may not have been done.
It is possible to get them to start by prolonged cranking until the oil pressure builds up but there is the danger of blowing out the Air Box.