External Apple cinema screen does not connect

Hi and HELP!
I have MacBookPro (with up-to-date software) and an external cinema screen. Without any changes to my set-up, the screen is no longer connecting, and I'm at my wit's end. The screen shows the white power light as on, and when I insert the connecting cable, the laptop screen briefly goes black as it does every time I connect the external screen. But the external screen then doesn't come up. It also doesn't show in Settings under Screens.

So, right now I have a connected cinema screen with its power light on, which is not recognised by my laptop.

Any ideas? Cables all seem fine, and I've restarted the laptop and switched off the power for a few seconds to reset the screen. Not success.

Many thanks!