```python
def driest_window(rain: list, width: int) -> int:
    if not isinstance(rain, list):
        raise ValueError("rain is not a list")
    if not all(isinstance(r, int) and r >= 0 for r in rain):
        raise ValueError("all readings are not non-negative integers")
    if not isinstance(width, int) or width <= 0 or width > len(rain):
        raise ValueError("width is not a positive whole number within the range of days")
    
    if width == len(rain):
        return 0
    
    min_sum = float('inf')
    start_index = 0
    
    for i in range(len(rain) - width + 1):
        current_sum = sum(rain[i:i + width])
        if current_sum < min_sum:
            min_sum = current_sum
            start_index = i
    
    return start_index
```