New Batteries, TI-83 will not turn on

Unfortunately, TI doesn’t offer any repair centers anywhere. If your calculator is still within warranty they will replace the unit, but if it’s out of warranty then you’ll have to pay for a new one. Your problem likely has a very easy fix so there shouldn’t be any need to contact TI yet.

1. This may be as simple as the contrast being too low. Turn the calculator ‘on’ as you normally would. Now press [2nd] then the up arrow multiple times. After a couple times of pressing [2nd] and the up arrow, the screen will appear again if the contrast was the issue.
2. If that’s not the issue then, as jostewcrew suggested, try changing out your backup battery. There’s a guide for accomplishing that here: Texas Instruments TI-83 Plus Backup Battery Replacement
3. If it still doesn’t turn on then there may be an issue with the screen itself. If you have the link cable that connects your calculator to your computer, install ‘TI Connect’ (Not ‘TI Connect CE’) on your computer then connect the calculator to your computer. (The port is on the bottom of the calculator and looks like a headphone jack). If your computer detects that your calculator is connected, then there’s something wrong with the screen itself. Likely the ribbon cable is degraded and needs repair. There’s a guide for fixing that on a calculator forum called Cemetech: https://www.cemetech.net/forum/viewtopic...
4. If your computer still doesn’t detect the calculator (make sure it’s on!) then there’s a more serious hardware issue and may not be diagnosable or fixable.

Hopefully you don’t need to get past step 2 but I wanted to cover all bases just in case. Good luck!