This is from TI FAQS:
Solution 11900: Troubleshooting a TI Graphing Calculator That Will Not Turn On.
For the TI-83 Plus Family, TI-84 Plus Family:
Caution: The resets described in these troubleshooting steps will cause a loss of applications, programs and data. If at all possible please create
a backup using TI Connect™ first.
- Try a new set of AAA batteries.
- Adjust the contrast by pressing and releasing the [2nd] key followed by pressing and releasing the up arrow; repeat as necessary. To adjust or lighten the display, use the down arrow.
- Remove one of the AAA batteries. Press and hold the [CLEAR] key. While holding [CLEAR], reinsert the AAA battery and then turn the calculator on. The calculator should display the message "RAM Cleared". Release the [CLEAR] key and then press it one more time to remove the message.
- Remove one of the AAA batteries. Press and hold the [DEL] key. While holding [DEL], reinsert the AAA battery and then turn the calculator on. The calculator should display "Waiting...Please install calculator software now". Follow the instructions for the TI-83 family or TI-84 Plus family to reinstall the calculator operating system.
- Remove all of the batteries including the round lithium battery for 5 minutes. After the 5 minute period, reinsert all of the batteries and turn the calculator on. Adjust the contrast if necessary.
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