Sure, here is a test case generator for the given problem statement:

```python
import random

def generate_valid_distance_matrix(N):
    """
    Generates a valid shortest distance matrix for a fully connected undirected graph with N nodes.
    """
    A = [[0] * N for _ in range(N)]

    # Generate a random distance matrix for the upper triangle
    for i in range(N):
        for j in range(i + 1, N):
            A[i][j] = random.randint(1, 10**9)
            A[j][i] = A[i][j] # Symmetric matrix

    return A

def generate_invalid_distance_matrix(N):
    """
    Generates an invalid shortest distance matrix for testing.
    """
    A = generate_valid_distance_matrix(N)
    
    # Introduce an inconsistency
    i, j = random.sample(range(N), 2)
    A[i][j] += random.randint(1, 10) # Make sure A[i][j] is not the sum of shortest paths

    return A

def tcgen():
    N = random.randint(1, 300)
    
    if random.random() > 0.5:
        A = generate_valid_distance_matrix(N)
    else:
        A = generate_invalid_distance_matrix(N)
    
    return N, A

# Example of generating test cases
N, A = tcgen()
print(N)
for row in A:
    print(' '.join(map(str, row)))
```

### Explanation:
1. **generate_valid_distance_matrix(N)**: This function creates a valid distance matrix for a fully connected undirected graph with `N` nodes. The distances are random integers between 1 and 10^9. It ensures that the matrix is symmetric and that the diagonal elements are zero.

2. **generate_invalid_distance_matrix(N)**: This function first generates a valid distance matrix and then introduces an inconsistency by modifying a randomly selected element to ensure it does not represent the shortest path.

3. **tcgen()**: This function randomly decides whether to generate a valid or invalid distance matrix and returns it along with the size `N`.

The generated test cases can be used to evaluate both the correctness and robustness of your algorithm for detecting valid and invalid road networks.