I'm not using whole numbers in my program though.  I'm using real numbers.
I also initialized my totals for each category to 0.00 so that it has a value to start off with before accumulations.  However, this doesn't solve the problem as my program is still giving me crap values.
Here's the code to make it more easier:
/* Prob 10-3
*  Created by Yuriy Mokriy
*/
#include <stdio.h>
#include <stdlib.h>
double Get_Opening_Balance();                                 /* Gets the user's opening account balance */
void Choice_Menu();                                           /* Displays a menu for choices */
void Validate_Choice(double);                                 /* Validates the user's choice from the menu */
double Deposit(double, double);                               /* Gets the user's deposit amount */
double Withdrawal(double, double);                            /* Gets the user's withdrawal amount */
double Check(double, double);                                 /* Gets the user's check amount */
void Display_Results(double, double, double, double, double); /* Displays all results and totals */
main()
{    
      double open_balance_amount;            /* The user's opening account balance */
      
      /* Call functions */
      
      open_balance_amount = Get_Opening_Balance();
      Choice_Menu();     
      Validate_Choice(open_balance_amount);
}
double Get_Opening_Balance()
{
      double open_acct_balance;              /* The user's opening account balance */
      
      /* Prompt the user */
      
      printf("\nEnter the opening account balance: $");
      scanf("%lf", &open_acct_balance);
      
      if (open_acct_balance < 0.00)
         exit(0);
      else
         return open_acct_balance;      
}
void Choice_Menu()
{
      /* Display menu */
      
      printf("\nSelect your choice: ");
      printf("\n(D)Deposit");
      printf("\n(C)Check");
      printf("\n(W)Withdrawal");
      printf("\n(Q)Quit");  
      printf("\n");  
}
void Validate_Choice(double opening_balance_amt)
{
      char choice;                           /* The choice entered by the user */
      double total_deposit_amt,              /* The total amount deposited */
             total_withdrawal_amt,           /* The total amount withdrawn */
             deposited_amt,                  /* The amount deposited */
             withdrawn_amt,                  /* The amount withdrawn */
             total_check_amt,                /* The total check amount */
             check_amt,                      /* The check amount */
             account_balance,                /* The current account balance */
             closing_balance_amt;            /* The closing balance amount */
             
      /* Initialization */  
       
      total_deposit_amt = 0.00;
      total_withdrawal_amt = 0.00;
      total_check_amt = 0.00;
      account_balance = 0.00;
      account_balance += opening_balance_amt;
          
      /* Get choice */
      
      getchar();
      choice = getchar();
      
      /* Validate choice */
      
      while (choice != 'q' || choice != 'Q')
      {
       if (choice == 'd' || choice == 'D')
       {
          account_balance = Deposit(deposited_amt, account_balance);
          total_deposit_amt = account_balance - opening_balance_amt - total_withdrawal_amt - total_check_amt;
       }
       else if (choice == 'w' || choice == 'W') 
       {
          account_balance = Withdrawal(withdrawn_amt, account_balance);
          total_withdrawal_amt = -(account_balance - opening_balance_amt - total_deposit_amt - total_check_amt);
       }
       else if (choice == 'c' || choice == 'C')
       {
          account_balance = Check(check_amt, account_balance);
          total_check_amt = -(account_balance - opening_balance_amt - total_deposit_amt - total_withdrawal_amt);
       }
       else if (choice == 'q' || choice == 'Q')
       {
         closing_balance_amt = account_balance;
         Display_Results(opening_balance_amt, total_deposit_amt, total_withdrawal_amt, total_check_amt, closing_balance_amt);
         exit(0);
       }  
       else
         printf("\nError! You must enter the following choices listed on the menu.");
         
         Choice_Menu();
         getchar();
         choice = getchar();
      }       
}
double Deposit(double deposit_amount, double pres_account)
{         
      /* Prompt the user */
      
      printf("\nEnter the amount to be deposited: $");
      scanf("%lf", &deposit_amount);
      
      pres_account += deposit_amount;  
      
      return pres_account;
}
double Withdrawal(double withdrawal_amount, double present_account_balance)
{   
      /* Prompt the user */
      
      printf("\nEnter the amount to be withdrawn: $");
      scanf("%lf", &withdrawal_amount);
      
      if (withdrawal_amount > present_account_balance)
      {
        printf("\nWarning! The amount you have withdrawn exceeds your current account balance.\n");
        exit(1);
      }
      
      else
      {
        present_account_balance -= withdrawal_amount; 
        return present_account_balance;
      }
}
double Check(double check_amount, double curr_account)
{       
      /* Prompt the user */ 
      
      printf("\nEnter the check amount $");
      scanf("%lf", &check_amount);
      
      if (check_amount > curr_account)
      {
        printf("\nWarning! The check amount exceeds your current account balance.\n");
        exit(1);
      }
      
      else
      {
        curr_account -= check_amount;
        return curr_account;  
      }
}
void Display_Results(double opening_balance, double total_deposit, double total_withdrawal, double total_check, double closing_balance)
{
      /* Display the results */
      
      printf("\nOPENING BALANCE:        $%.2lf", opening_balance);
      printf("\nTOTAL AMOUNT DEPOSITED: $%.2lf", total_deposit);    
      printf("\nTOTAL AMOUNT WITHDRAWN: $%.2lf", total_withdrawal);
      printf("\nTOTAL CHECK AMOUNT:     $%.2lf", total_check);
      printf("\n----------------------------------");
      printf("\nCLOSING BALANCE:        $%.2lf", closing_balance);
      printf("\n");
}