Code:
$ ./a.out 
  0   1   2   3   4   5   6   7   8 
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 0
+---+---+---+---+---+---+---+---+
|L12|   |L11|   |L10|   |L9 |   | 1
+---+---+---+---+---+---+---+---+
|   |L8 |   |L7 |   |L6 |   |L5 | 2
+---+---+---+---+---+---+---+---+
|L4 |   |L3 |   |L2 |   |L1 |   | 3
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 4
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   | 5
+---+---+---+---+---+---+---+---+
|   |D1 |   |D2 |   |D3 |   |D4 | 6
+---+---+---+---+---+---+---+---+
|D5 |   |D6 |   |D7 |   |D8 |   | 7
+---+---+---+---+---+---+---+---+
Why is there an 8 at the end of the top row?
Why are there 3 rows of L pieces?
Why don't the L pieces start in the first row?

/* If the value of board[i][j] is equal to 1, then that piece is Player 1's piece.
If the value of board[i][j] is equal to 2, then that piece is Player 2's piece.
board[i][j] is equal to 0 means that the location is not an outer bound area, (white squares)
board[i][j] is equal to 3 means that the location is a possible position but is empty */
Use an enum.
Code:
enum {
    EMPTY = 0,  // unused space
    WHITE = 1,  // white piece
    BLACK = 2,  // black piece
    FREE = 3,  // valid, but unused position
};
...
            if(((i == 6)&&(j%2 == 1))||((i == 7)&&(j%2 == 0))||((i == 8)&&(j%2 == 1))) //Player 1 Pieces; valid square value is changed to 1
            {
                board[i][j] = WHITE;
            }            
            else if(((i == 1)&&(j%2 == 0))||((i == 2)&&(j%2 == 1))||((i == 3)&&(j%2 == 0))) //Player 2 Pieces; valid square value is changed to 2
            {
                board[i][j] = BLACK;
            }   
            else if((i + j)%2 == 1) //Checks all Valid Squares and value is set to 3
            {
                board[i][j] = FREE;
            }          
            else
            {
                board[i][j] = EMPTY;
            }