Firstly check the battery compartment for any sign that the old batteries have leaked. Look for signs of corrosion, white powdery deposits on any of the contacts? You can clean the contacts with a little alcohol or a light abrasive. Also check they are in the correct way round!! Next you can reset the calculator as described on page 740 of the manual which you can download below: http://education.ti.com/guidebooks/graphing/83p/83m$book-eng.pdf The full reset of the calculator is as per this diagram:
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.
Just keep trying. Sometimes they can be a pain.
Usually answered in minutes!