Can you have fuel pressure but the computer doesn't tell injectors to squirt fuel into cylinder?

 

Yes. The computer has no idea if you have fuel pressure or not. It's not a parameter the computer can see.

What controls the injectors firing are things like throttle position sensor, crank position sensor, cam position sensor stuff like that.

 

Yes you can. If the ASD relay doesn't energize, you won't get spark or injector pulses. Normal starting cycle is turn on the key and the fuel pump runs for about 2 seconds just to charge the fuel rail with pressure, then shuts off. When you start cranking it, the computer waits to get a signal from the CKS that the crank is actually turning, then it energizes the ASD and fuel pump relays. As soon as the engine catches, the computer checks to see if the key is a valid one thru the SKIM module (If you have that function) and that the immobilizer isn't set, then allows it to stay running. If the computer doesn't receive signals from the CKS and CMS, it will cut the fuel pump relay and the engine will run until fuel pressure is lost, then quit.

CKS = crank sensor
CMS = cam sensor (As stated in the factory service manual.)

 

how does the computer get grounded? By it being mounted under the dash?

 

It's not under the dash it's bolted to the driver's fender in the engine bay next to the airbox.

 

Do we have any idea what year this Jeep is?

 

I understand that, but if the computer is not mounted to anything and is just hanging is it grounded?

 

1989

 

Yes.
Go to www.cruiser54.com and complete Tip 1.

 

You specifically said "Under the dash" so I was unsure what you did or didn't know about XJs.