HP 19bii Problem with the screen

[burkhard]

There's an active thread just (at the moment) near this one entitled "HP-28S battery door".
If you go into that thread, there's a gentlemen in Brazil who repairs HP calculators.

Take a look at his "before and after" pictures with center spots on the displays of a 42S and a 32SII that look similar to that on your 19BII:

http://hpcenter.com.br/fotos.html

I expect paying for such a repair isn't worth it for a 19BII, but the trouble does look similar.
If it were too annoying to live with, I would use it as a learning experience in fixing clamshell calculators.