My 1996 XJ6 runs, then will die. It starts right back up again but will then die again. This is an intermittent problem. I took the car to a professional mechanic. He said that there was a ground fault and that the computer needed to be replaced. Does anyone know if this sounds reasonable or is the mechanic full of crap? Thank you!

 

I would suggest the ground fault needs to be remedied before coming to any other conclusions. They are not uncommon in X300s and can cause a wide and often seemingly random range of problems.
The earth for the ECU is easily checked, if you pull back the carpet in the front of the front right hand footwell at the right hand edge. There are many other earths, and a " map" of these was posted here in the last few days. Worth checking them all.