Alright, I have a code that now works.
But like always I have a couple problems I'm still seeking help with on it.

1. Every time I want to login I have to register a new account. And after I do that and login, If I try to login again it says "Invalid username or password." It's like the file is deleting any information that is sent to it.

So I'm trying to find a way to permanently store data once I have registered an account so that anytime I run the program I can always just login with an account I already made.

Here is my header code:
Code:
#ifndef CHARACTERINFO_H_INCLUDED
#define CHARACTERINFO_H_INCLUDED

class Character
{
    public:
    char name[16];
    char pword[10];

        void sendNAME();
        void sendPWORD();
};

#endif // CHARACTERINFO_H_INCLUDED

Here is my source code:

Code:
#include <iostream>
#include <fstream>
#include "CharacterInfo.h"
using namespace std;

void Character::sendNAME()
{
    cout << "Enter your desired username(max 16 characters): ";
    cin >> name;
    cin.ignore(numeric_limits<streamsize>::max(), '\n');
};

void Character::sendPWORD()
{
    cout << "Enter your password(max 10 characters): ";
    cin >> pword;
    cin.ignore(numeric_limits<streamsize>::max(), '\n');
};

int startMenu()
{
    int option;
    cout << "Welcome to the login menu..." << endl;
    cout << "\tPress '1' to login." << endl;
    cout << "\tPress '2' to register." << endl;
    cout << "Your option: ";
    cin >> option;
    cin.ignore(numeric_limits<streamsize>::max(), '\n');
    return option;
};

int main()
{
    ifstream readFile ("example.txt");
    ofstream writeFile ("example.txt");
    Character charInfo;
    do
    {
        int option = startMenu();
        cout << endl;

        if(option == 1)
        {
            string username;
            string password;

            cout << "Enter Name: ";
            cin >> username;
            cout << "Enter Password: ";
            cin >> password;
            cout << endl;
            string temp;
            while(readFile>>temp)
            {
                if(temp == charInfo.name)
                {
                    readFile>>temp;
                    if(temp == charInfo.pword)
                    {
                        cout << "Welcome " << username << "!" <<endl;
                        break;
                    }

                }
                else
                {
                    cout << "Invalid username or password." << endl;
                }
            }
        }
        cout << endl;
        if(option == 2)
        {
            charInfo.sendNAME();
            cout << endl;
            charInfo.sendPWORD();
            cout << endl;
            if (writeFile.is_open())
            {
                writeFile << charInfo.name << ' ' << charInfo.pword << endl;
                writeFile << charInfo.pword;
                writeFile.close();
            }
            else
            {
                cout << "Unable to open file";
            }
        }
    }while(1);
    return 0;
}