Initialize the results array so all elements are NULL:

char* results[10] = { NULL };

In the posted code the elements are unitialized and will be holding random values.

Additionally, prevent going beyond the bounds of the results array:

while (i < 10 && result)
{
}

An array in C++ cannot be null; only a pointer can be null.

To test whether a pointer is null, you simply test whether it compares equal to NULL or 0.

You're right, that is a pointless check, if done in the same context.

If you pass it as parameter to a function, the the array decays into a pointer and it's not so pointless.

what should go there instead to check the array is empty

Well, the array is never empty. It will always contain MAX_LOGPATH_LEN TCHARs. But the following could do the trick:

if( m_sLogPath[0] == _T('\0') || _tcsicmp(m_sLogPath, trace_path)!=0)

What do you mean with empty?

When a C program is executed, variables that you don't explicitly initialize have got unpredictable values.

You need to set all of your array cells to NULL (or to 0, or to whatever value represents emptyness in your program logic) and then you can check it in the way you did:

int *array[3] = { NULL, NULL, NULL }; // array of three "empty" pointers

...

for( i = 0; i < 3; ++ i ) {
  if( array[i] == NULL ) {
    // i-th cell is "empty"
  }
}

You should add a "check" in your "modify" function.

Original:

void ModifyValue(int a[]){
int modification,position;
cout<<"Enter the position of a number to modify";
cin>>position;
cout<<"Enter a number to modify";
cin>>modification;
a[position-1]=modification;

With "check":

void ModifyValue(int a[]){
//Check
if(count == 0)
{
   cout << "Sorry no value added so far";
   return; //Exit from function
}

int modification,position;
cout<<"Enter the position of a number to modify";
cin>>position;
cout<<"Enter a number to modify";
cin>>modification;
a[position-1]=modification;
}

Also I recommend you to use switch instead of "if else if"

if (n==1){
    AddNewValue(a);         //calling functions using if else statments
}
else if(n==2){
    SearchValue(a);
}
else if(n==3){
    ModifyValue(a);
}
else if(n==4){
    PrintValue(a);
}
else if(n==5){
    PrintSum(a);
}

like:

switch (n)  
  {  
     case 1:  
        AddNewValue(a);  
        break;

     case 2:  
        SearchValue(a);  
        break;

     case 3:  
        ModifyValue(a);;  
        break;

     //And so on...

     default:  
        cout << "Unknown option";  
  }

Also in this code you don't need any arguments in

  void menu(int n)

So you can make

  void menu()

instead.

Also I recommend you to place whitespaces between operands and operators (words)

cout << "Enter a value\n";
cin >> a[count];  //taking input to array
count++;

instead

cout<<"Enter a value\n";
cin>>a[count];  //taking input to array
count++;