The TLC5940's and arduino are powered off a computer power supply.
That computer power supply probably delivers 5V and 12V. Which one are you using and to which connector do you have it connected? That's what I mean by wiring: describe every wire going to or from the Arduino. Tell us which pin/connector you use on the Arduino and where it goes to. Connecting multiple grounds usually isn't a problem. So it must be somewhere else.