Like a number of other S Type owners, I have suffered from periodic Parkbrake failure, sometimes with the Parkbrake on and sometimes off. The former immobilises the vehicle which can be quite inconvenient. In both cases the situation has been resolved by disconnecting the neutral connection from the battery, short-circuiting the vehicle circuit for about 30 seconds and then reconnecting. It is best to leave the key in the ignition in the "off" position as you do this, as otherwise the alarm can go off, and you need to re-set the parkbrake and input the radio code etc. This method has never failed to sort the problem.
Recently however, the incidence of parkbrake failure has become greater and really quite annoying ( and sometimes embarrassing!). It also became apparent that it invariably occurred on start-up, as I cranked the engine. Having already changed the 9-year old battery, and checked the connections I came to the conclusion that the cause of the problem was the starter motor. I have just had my local non-jaguar workshop change this item (for about £330 inc VAT) and you wouldn't believe the difference in cranking speed and starting performance. Even the mechanic was surprised at the difference. Although I have started the car on only a few occasions since I am confident that this has effected a permanent cure.
Having owned the car from new and covered 109,000 miles I had not appreciated the gradual deterioration in starter motor performance, which was almost certainly causing the voltage-drop that affects a number of electronic systems. If readers have a parkbrake problem I would recommend that you consider replacing the vehicle's starter motor, probably before the battery unless it is very old.
If I do suffer a recurrence I shall post an additional comment. However, I am sure that will not be necessary.