If a car has been setting idle for a long time, it is very common for the
automatic transmission to be sticky in shifting. It nearly always goes away
soon, you just have to be careful not to over-rev the engine or let the
transmission slip too much when it is acting up. Some transmission solvent
in the oil can help as can having the transmission oil and filter changed.

Don Young

The Prof wrote:

I've just bought a similar car, age and mileage - same problem. I find
it difficult to select Drive and Reverse especially when the car is
cold, no problems otherwise apart from a bit of a petrol smell when I
start in the morning. I'd take it to the garage, but am in a battle
with the supplier who promised a warranty but haven't sent it yet.
They don't know I'm a lawyer but they will soon!

Let me know if you discover what's wrong with your Jag. With the
exception of the above, the car is great.

Richard

Take it to an auto box specialist, sounds like something sticking,
occassionally, which a test will not show unless the problem occurs whilst
being tested.
PS How is reverse when this occurs?

Have recently purchased  a 2000 S-Type, excellent condition, well looked
after, 85000km on the clock. Always Jag serviced. Drives beautifully 98%
of the time, but every now & then will not shift into gear when put into
Drive, and the indicator light is showing "D". Then, when it does get
moving, it plays up shifting from 1st to 2nd.

  Have taken it to the local Jag dealer, no faults have been logged,
and all tests are normal.

  Anyone got any ideas, or had anything similar?