[hardwired]

The main method does not go inside any other method or constructor.
It stands by itself as a method inside a class body, viz, the curley braces {}.
Compile errors:

Code:

C:\jexp>javac bankingrx.java
bankingrx.java:46: cannot find symbol
symbol  : method validWithdrawal(double)
location: class CustomerRx
                    cust.validWithdrawal(withdrawal);
                        ^
bankingrx.java:49: cannot find symbol
symbol  : method showMessageDialog(java.lang.String)
location: class javax.swing.JOptionPane
                    JOptionPane.showMessageDialog("Your remaining balance is:" +

                               ^
bankingrx.java:53: cannot find symbol
symbol  : variable output
location: class BankingRx
                    JOptionPane.showMessageDialog(null,output,"not valid choice"
,
                                                       ^
3 errors

Comments in code below show how these were fixed.
I changed the names of the classes so you can run this as–is.

Code:

import java.io.*;
import javax.swing.JOptionPane;
import java.text.DecimalFormat;

public class BankingRx 
{
    public BankingRx() {}

    public static void main(String[] args)
    {
        //Housekeeping
        int depCount = 0, withdrawalCount = 0, choices;
        double startingBalance = 0, deposit = 0, withdrawal = 0;
        boolean validWithdrawal = true;

        DecimalFormat twoDigits = new DecimalFormat("0.00");

        //Processing
        CustomerRx cust = new CustomerRx(); //Instantiate customer object

        // populates the starting balance field with
        // accountBalance from customer class
        startingBalance = cust.accountBalance;

        do
        {
            choices = Integer.parseInt(
                          JOptionPane.showInputDialog("Menu :\n" +
                                           "Enter 1 - For Deposit\n" +
                                           "Enter 2 - For Withdrawal\n" +
                                           "Enter3 - For Balance\n" +
                                           "Enter 9 - To Terminate\n"));

            switch(choices)
            {
                case 1:
                    deposit = Double.parseDouble(
                                  JOptionPane.showInputDialog("Pl ease enter " +
                                                              "a deposit amount."));
                    cust.processDeposit(deposit);
                    break;
                case 2:
                    withdrawal = Double.parseDouble(
                                     JOptionPane.showInputDialog("Pl ease enter " +
                                                                 "a withdrawal."));
                    // CustomerRx class does not have this method.
//                    cust.validWithdrawal(withdrawal);
                    break;
                case 3:
                    // JOptionPane class does not have a method that takes
                    // these type of arguments.
//                    JOptionPane.showMessageDialog("Your remaining balance is:" +
//                                                   cust.accountBalance);
                    // Try this
                    JOptionPane.showMessageDialog(null,"Your remaining balance " +
                                                  "is:" + cust.accountBalance);
                    break;
                default:
                    // Variable "output" has not been declared.
                    String output = "hello world";
                    JOptionPane.showMessageDialog(null,output,"not valid choice",
                                                  JOptionPane.INFORMATION_MESSAGE);
            }

            String output = "Customer Name : " + cust.customerName + "\n";
            output += "Customer Account # : " + cust.customerAcct + "\n";
            output += "Starting Balance : " + twoDigits.format(startingBalance) + "\n\n";
            output += "Total Deposit : " + twoDigits.format(cust.totalDeposits) + "\n";
            output += "Total Withdrawal : " +
                       twoDigits.format(cust.totalWithdrawals) + "\n\n";
            output += "Closing Balance : " + twoDigits.format(cust.accountBalance) + "\n";

            JOptionPane.showMessageDialog(null, output, "Transaction Summary",         
                                          JOptionPane.INFORMATION_MESSAGE);
//            System.exit(0);
        } while (choices != 9);        
    }
}

class CustomerRx
{
    // member variables in class scope
    String customerName;
    int customerAcct;
    double accountBalance, totalDeposits, totalWithdrawals;

    //constructor
    CustomerRx()
    {
        customerName = JOptionPane.showInputDialog("Please enter the Customer's name");
        customerAcct = Integer.parseInt(
                           JOptionPane.showInputDialog("Plea se enter the " +
                                                       "Customer's Account Number"));
         accountBalance = Double.parseDouble(
                              JOptionPane.showInputDialog("Pl ease enter the " +
                                                          "starting balance"));
         totalDeposits= 0;
         totalWithdrawals=0;
    }

    //methods
    void processDeposit(double depositAmount)
    {
        accountBalance += depositAmount;
        totalDeposits +=depositAmount;
    }

    boolean processWithdrawal(double withdrawalAmount)
    {
        if (withdrawalAmount <= accountBalance)
        {
            accountBalance -= withdrawalAmount;
            totalWithdrawals += withdrawalAmount;
            return true;
        }
        else
        {
            String errorMessage = "Insufficient Funds!! ";
            errorMessage += "Your current balance is " + accountBalance;

            JOptionPane.showMessageDialog(null, errorMessage, "Error",
                                          JOptionPane.ERROR_MESSAGE);
            return false; 
        }
    }
}