My son and I have come across dozens of dead TI's and the only one that we couldn't fix was a TI nSpire first version. All of the others were contacts, corrosion, or pencil leads stuck in the comm port making the calc reboot in a loop.
I’ve been trying to get inside of my ti-89 titanium for some time now to see why my calculator won’t turn on. Which size screw driver bit are you using to open them?
It's always a good idea to open it up and clean any corrosion if there's any. Also, make sure all the metals in the battery compartment are in full contact with the terminals. This can cause numerous unexpected issues.