Have you tried just cranking without throttle to see if it eventually starts? Sounds like fuel pump as the fitler AND check valve are built in. Once it's running if you turn it off does it start up right away?
Try this next time it's been sitting. Without starting key the ignition to on, then off, then on, then off a couple times. Every time you key on the pump will run to prime the system. If it starts fine like this the problem is the pump. The plus side most XJs you can replace the pump without dropping the tank. It's a tight space but doable. Also worth noting make sure you have less than half a tank if you're going to do it this way...I shouldn't have to explain that one any further.