I'm willing to bet the internal battery is shot, as is in mine. I'm sure you have swapped the main batteries 4 AAA's if I remember correctly. If you look directly above those you will see a little screw and should be able to replace the internal battery. I don't have the exact version, as I have a TI84 Plus, but I remember the battery compartment being very similar.
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It could be than that the logic board final went kaput. :( I know my buddies went out in a similar fashion. His started having screen graphic issues, than would die soon after replacing the batteries. Have you tried calling Texas instruments to see if maybe they have any other possibilities? Sorry that unless I have the device, and take a look at some of the terminals, I can't think of any possibilities.
I'm willing to bet the internal battery is shot, as is in mine. I'm sure you have swapped the main batteries 4 AAA's if I remember correctly. If you look directly above those you will see a little screw and should be able to replace the internal battery. I don't have the exact version, as I have a TI84 Plus, but I remember the battery compartment being very similar.