How are these LEDs and their associated resistors wired.
This is the data sheet:- TLC5940 LED PWM Driver.pdf (932.4 KB)
If you look at page 8 you will see that the output can behave in a few different ways. This will determine how you have to wire up your LEDs and resistors.
This is a rather old chip, almost obsolete now.
Your wiring diagram shows no other connections you need to drive this chip.
I am sure you are missing other stuff like setting which output configuration to use.