Charlieplexing ( LoL Shield library) and DS3231 RTC (Chronodot) CONFLICT HELP!

Let's see if it is a problem with ram.
Add this function to your code:

int freeRam () {
  extern unsigned int __heap_start, *__brkval; 
  int v; 
  return (int) &v - (__brkval == 0 ? (int) &__heap_start : (int) __brkval); 
}

And then put

Serial.print(F("freeRam = "));
Serial.println(freeRam());

immediately after Serial.begin() in setup()

Run the code with the call to LedSign::Init() commented out and then run it again with it in and see what values are printed for freeRam.
You might also try putting LedSign::Init() after the Wire.begin() to see if that makes any difference.

Pete