My 4000 had 2 black display failures
(I assume you have a copy of the service manual)
In the bottom right corner of the IO, VR Circuit Schematic transistors TR1 and 2 that control the -24V line of the display, seem to be a common point of failure.
These transistors DTC144ES have integrated resistors, which makes them rather uncommon parts.
In my case someone bridged one of them (an old repair I discovered only after purchase) and if that bridge is removed, the display stays dark.
The 2nd case was myself killing an opamp on the display electronic while fiddling with a worn ribbon cable (machine powered up).
Iirc an LM358, but it‘s the only opamp (SMD, 8 pins) on that board, so just refer to it‘s label. I mention it for completeness, imho a rather unlikely case.
But in my case the LEDs never stayed in lit stage, so your case is probably different.
Regarding the display ribbon:
if the damage is right at the connector, it can be „repaired“, but with a lot of patience.
Snip off the end of the ribbon in a precise 90 degree cut and then remove the isolation plastic on the side which is supposed to do the connection.
I carefully scratched off the isolation with a mixture of using a sharp blade and very fine sanding paper. The ribbon was fixed to the table by some double adhesive tape.
Good light and a magnifier needed to stop at the proper depth.
(you just have to get the conductive ink free from isolation)
Finally I added some very thin tape to strengthen the backside of the new connection.
