Back to reply #3: Try using lower value pullups. The TLC5940 datasheet says it needs to sink 5mA minimum - with your 10K, you're only getting 0.5mA.
Change to 1K, 820, something like that.
Also try putting an inverter between the '5940 and the 2803 (say, another 2803!) so that when the 5940 is low the output of the 2nd 2803 is also low.