Hi this sounds like a hardware problem. Unfortunately, unlike the TI 83 and TI 84 lineup, the TI 89 ti doesn’t have a standard ribbon cable you can fix, instead TI attached everything to one piece making it nearly impossible to fix yourself. Even the most skilled calculator enthusiasts I know haven’t been able to repair a TI 89 ti display. :(
I’m sorry I wasn’t able to help you repair it, however if you have any other questions I’ll be happy to answer them.