Thanks for the input guys. I went back and started from scratch, ended up attaching the Power Supply's "+" and "-" to the breadboards "+" and "-" lines while leaving the Arduino's +5V and Gnd Plugged into the same lines and its all working.
As for the power dissipation the TLC5940 datasheet say's it has a power dissipation of 2.5W- fungus you stated 1.5W is this just incoraporating a safety margin?
My LED's use 3.2V at 120mA so 5V-3.2V = 1.8V.... 1.8V * 120mA == 0.216W per channel. 2.5W/ 0.216W = 11.57 ..... So I can run 11 of these LED's.
Putting these numbers into this site: http://led.linear1.org/led.wiz -advises that I use a 15ohm resistor on each channel in order to run all 16 of LED's.
Hopefully that will work- I haven't accounted for the current the TLC uses and am new to this so might be completely wrong!