From your symptoms, my guess would be a bad/plugged catalytic converter,
possibly brought on by the bad coil pack. But, I'm no expert.

Hello,

Question, did they replace the spark plugs too?

I think Wayne may be correct, and those sparks may have been a result
of the converter matrix melting. If you have been surfing around the
various Jag forums you probably might have noticed many similar
stories.

They seem to go:
"Started with a valve cover leak which filled the spark plug holes,
coils failed, cats failed."

Description: (Taken from Tenneco)
<begin> For the entry level Jaguar 3.0 V6 model through to the
flagship of the range, the 4.0 V8, Tenneco has developed a twin close
coupled catalytic converter and muffler. In addition, for the V8 the
company has designed a fabricated air gap insulated manifold which has
enabled Jaguar to do away with the traditional heat shield which
protects surrounding parts such as the cam cover, steering column and
so on. A further advantage of the new manifold is the reduction of
light-off time for close coupled converters and semi close coupled
converters, offering the capability to achieve more stringent emission
standards.

As far as the catalytic converter is concerned, the Jaguar S-type
system has been fitted with a monolith converter designed specifically
to generate significantly less back pressure and improve engine
output. Twin close coupled catalysts deliver low emissions and good
fuel economy. <end>

If the converters did fail, take care to inspect for signs that the
converter might have blown chucks of matrix into your mufflers
resulting with back pressure/blockage. Also it is absolutely stressed
to replace your O2 sensors when changing a cat!

It's going to be expensive and taking shortcuts may be like throwing
money to the wind.

Best Regards,
Blake