Hi @howardant ,
With the tablet turned on but having a black display, try shining a torch at an angle close to the screen and check if you can detect any images at all.
They will be very faint if they are there, so trying this in a darkened room may help to see them.
If you can detect images then there is a backlight problem.
Here’s the Ifixit Samsung Galaxy Note 10.1 2014 Screen Replacement guide. This will help you to check if the display’s flex cable connection to the systemboard is secure.
If the cable is secure then you can either:
Replace the LCD screen and check if it now works OK . Search online for Galaxy Note 10.1 2014 LCD screen to find suppliers that suit you best.
Use the No LCD troubleshooting section of the schematics for the tablet to locate whether the problem is on the systemboard or in the display assembly so you know whether a replacement display is required or that the problem is on the systemboard.
(click on image to enlarge).
Hopefully this is of some help.