Sure, I can help you write a test case generator for the given problem. The generator will create random values for \(N\), the array \(A\), and the cables connecting the devices. Here is a Python function to generate test cases for the problem statement:

```python
import random

def tcgen():
    # Generate N
    N = random.randint(1, 5000)
    
    # Generate the array A with non-zero integers between -10^9 and 10^9
    A = [random.randint(-10**9, 10**9) for _ in range(N)]
    # Ensure no zero values in A
    A = [x if x != 0 else 1 for x in A]
    
    # Generate the cables
    cables = []
    available_nodes = [i + 1 for i in range(N)]
    random.shuffle(available_nodes)
    
    for i in range(1, N):
        u = available_nodes[i]
        v = available_nodes[random.randint(0, i-1)]
        cables.append((u, v))
    
    return N, A, cables

# Example of generating a test case
N, A, cables = tcgen()
print(N)
print(" ".join(map(str, A)))
for u, v in cables:
    print(u, v)
```

### Explanation
1. **Generating \(N\)**: Randomly choose \(N\) between 1 and 5000.
2. **Generating the array \(A\)**: Create an array of \(N\) integers where each integer is a non-zero value between -10^9 and 10^9.
3. **Generating the cables**: 
    - Create a list of node indices from 1 to \(N\).
    - Shuffle the list to randomize the order of nodes.
    - Connect each node to a random previous node to ensure the structure remains a valid tree.

This generator ensures that the test cases adhere to the constraints and structure defined in the problem statement. You can run the `tcgen` function to generate multiple test cases for testing purposes.