Have you tried applying a little pressure with your thumb on different areas of the display. Sometimes this will activate a dead screen for a split second. If this works then it's time to take the scanner apart and check for loose parts.
The light and the display are two different units.
My little Sportys JD100 was a gift in 1999 and the display was always problematic right from the start. I like this airband scanner and have used it a lot, even this afternoon I listened to it while in my shop. If I needed to know what frequency was active I could press on the lower portion of the display and all the digits would appear. About 2 months ago I was bored and decided to take it apart to look at the display and found that the two screws were slightly loose. A half turn each and the display works great for the first time ever.
Emboldened by this I tackled the Pro-60 which the display was missing the 3, 4, and 5...same thing, a loose screw. It now also works just fine.
Your mileage may vary, but it's something to think about. Besides these scanners and HT's are pretty simple to disassemble.
Good Luck
Ron