Wont turn on when new batteries were installed

Hello,
It is likely that the calculator is ON, but the screen is too light to enable user to see anything. If that is the reason, you can darken the screen.
Press the [2nd] key and release it. Press and hold the UpArrow till screen darkens enough.
If that does not work, here is what the Texas Instruments Knowledge Base says about the calculator not turning on.

Here it is from the horse's mouth (TI Knowledge base)

I hope it helps.

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.

1. Try a new set of AAA batteries.
2. Adjustthe 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.
3. 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.
4. 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 TI83-family or Ti84 Plus family to reinstall the calculator operating system (see below.)
5. 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.

Reinstalling the OS fot the TI84Plus

How do I correct the Error Waiting...Please Install Calculator SoftwareNow message on my TI-83 Plus family or TI-84 Plus family calculator?

If an operating system (OS) update fails or is interrupted, the calculator will be in an inoperable state with the message Waiting...Please install calculator software now.The most common cause of a transfer being interrupted is updating the operating system on a calculator with low batteries. Users will need touse the TI Connectivity cable and the TI Connect to send the operating system to the calculator. Make sure to have the latest version of TI Connect installed on the computer.
In order to install the software please follow these steps:
1. Connect the TI Connectivity cable between the computer and the calculator.
2. Click on Start >> Programs >> TI Tools >> TI Connect >> TI OSDownloader
3. Follow the on-screen directions to reinstall the calculator's OS.
If the message "Error! Press any key to turn unit off. Then turn unit back on." appears on the graphing calculator, quickly, remove one battery from the calculator and reinstall it while the transfer is taking place.