A lot of us experience gremlins with the convertible roof now and again, but my car's problem came down to the hydraulic pump (which powers almost all of the moving parts in the convertible roof and tonneau). The one part of the roof that the hydraulic pump doesn't operate is the latching mechanism at the connection to the windshield, which was the one piece that was working for me.

Here are the steps I went through to try and work out why it just wasn't working!
(#1 everytime!) Is the battery ok?
Check that your luggage compartment separator is in place and has the metal piece on the left hand side) and the trunk/boot is closed
Inspect to see if something is preventing the roof from moving?
Are there any leaks around the hydraulic pump, or underneath the car where the actuators on the rear sides of the roof are? It could be leaking hydraulic fluid form somewhere. (If so, jump to the end!)
Check the fuses for the roof (behind the rear seat armrest back)
Try resetting the roof computer: disconnect the battery for a minute, reconnect the battery, manually put the top in the open position in the trunk, start the car, reset the front windows by putting them up and down three times each while holding the button for 3 seconds after the window stops moving in each direction, try the roof again.
Is anything happening at the hydraulic pump in the trunk when operating the roof button (phone recording in closed trunk is helpful here). If relays are clicking then at least the computer may be trying to make things happen. In my case the solenoids got very hot.
Can the Jaguar SDD help identify the problem? I got the British Diagnostics cable and software, which is a great software with zero documentation and an interface that is not the most intuitive! If you need help with this, I'll be happy to offer my limited experience via PM or tag me. I asked for help from Andrew, the chap at BD but never got a reply.
Having tried the troubleshooting steps in the SDD (testing resistances of the wires running between the roof computer - located behind the left rear passenger seat - and the hydraulic pump)
Try taking out the hydraulic pump and connecting 12v to the larger connector on it. Be aware that this pump draws dozens of amps in normal operation so a small 12v battery may not provide enough juice. I used the car battery (be careful not to touch the ends together!)

If you've got to here, I can highly recommend getting in touch with Top Hydraulics in Oregon (https://www.tophydraulics.com/). They have videos on Youtube for our particular car, as well as other brands. In addition to the pump, Top Hydraulics has videos and parts for the actuators and other parts of the mechanism.

For $700 + shipping, I got my refurbished better-than-new hydraulic pump back in a week, which I expect will outlive the car. I can only imagine how much it would have cost me at a dealership to diagnose, let alone fix this roof problem. I'm no mechanic, but am keen to learn about my pride and joy of a car, and let me tell you that this whole process was not beyond my capabilities. It did test my patience at times.... however: if I can fix my roof, you can too!