I don't understand what you mean by reset pin and why there are so many. Can you draw a schematic of how you have wired things up. Is this the latch pin?
The LEDs attached to a shift register should not go out by themselves, you just strobe them when you are ready to change them.
You should get all the bits into one array and then output them all at the same time. Your code looks way over complex and I can't follow what is going on. It is far too verbose.
Have you got decoupling capacitors on the power supply pins of all chips?