Tinkerkit DMX shield can't use digital pin 4 for IO

The DMX shiled diagram you linked...

J1 and J3 (top/left) are connected to Uno pins 0-13, but they are numbered differently.

Start from the right (J1) with 0(RX), 1(TX), etc.
You see that pin 0-6 is used. 7-13 is free (the next pin is ground).

A2 is also used (analogue connector, left side).

Power connector should be obvious.
Leo..