No output or invalid output on a 74HC595 shift register
Which pins on the micro did you connect the extra shift registers to?

Do you use separate routines to talk to each set of shift registers?

Things to check:

1) Short, heavy ground wire between the extra shift registers and the main board (with the micro on it).

2) decoupling capacitor(s) at the shift registers.  

3) clock edge vs data change.  You can safely change the data line and clock line at the same time so long at that clock edge is the NOT-active edge.  That is: the clock line is going from HI to LO.  

However, you must allow sufficient setup time for the data level before you assert the active clock edge (LO to HI).

Long wires can exacerbate this problem - the clock line has higher capacitance because you are feeding multiple chips.  The data line feeds only one chip.