red_car,
You are correct! I found that I had to alter the if statement to say (currentMillis >476) in order to get the LED to turn on at a time close enough to the desired time. I played with the number in order to verify it's effect on the result. Thank you! I appear to be back in business.
unsigned long currentMillis = millis(); //unsigned long
unsigned long seconds = currentMillis / 1000; //unsigned long
unsigned long minutes = seconds / 60; //unsigned long
unsigned long hours = minutes / 60; //unsigned long
unsigned long days = hours / 24; //unsigned long
currentMillis %= 1000;
seconds %= 60;
minutes %= 60;
hours %= 24;
if(minutes == 3 && seconds == 36 && currentMillis >476)
{
digitalWrite(ledPin, HIGH);
}