Try using the digital PWM pins for your outputs, not the analog pins.
Change your #defines to use digital pins 9,10, and 11 (or any other three of the Digital pins with PWM capability: 3,5,6,9,10,11). And of course connect your interface board to the Arduino using these pins.
Also, in your test sketch there is really no need to use the map() statement, or to reinitialize the variables each time through the loop.
Try this for testing your basic interface board and Arduino PWM pins:
#define REDPIN 9
#define BLUEPIN 10
#define GREENPIN 11
int r = 0, g = 0, b = 0;
void setup() {
pinMode(REDPIN , OUTPUT);
pinMode(BLUEPIN, OUTPUT);
pinMode(GREENPIN, OUTPUT);
}
void loop() {
while(r<=255) {
analogWrite(REDPIN, r);
analogWrite(GREENPIN,g);
analogWrite(BLUEPIN, b);
r++; g++; b++;
delay(50);
}
r=0; g=0; b=0;
}
This should fade your LEDs from zero to full brightness smoothly in about 13 seconds, then start over from zero. (Tested on a ProMini).
Of course if you want to control the individual colors using potentiometers and the analogRead(analogPins) then you'll need the map() statements.