I just got a TI-83 Plus and turns out YOU CAN PROGRAM IT!
I went ahead and made a Number Guessing Game for my first go around. FUN!
Replace -> with the STO key
Disp "GUESS THE NUMBER"
Disp "TOO HIGH"
Disp "Too Low
Remember, TIBASIC is non whitespaced, so get rid of the spaces. Greater than, Less than, and Equals to can be found under CATALOG.