unit ClientUnit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls, IdBaseComponent, IdComponent, IdTCPConnection, IdTCPClient;

type
  TForm2 = class(TForm)
    IdTCPClient1: TIdTCPClient;
    host: TEdit;
    SendBtn: TButton;
    send: TEdit;
    ans: TEdit;
    port: TEdit;
    procedure SendBtnClick(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form2: TForm2;

implementation

{$R *.dfm}

procedure TForm2.SendBtnClick(Sender: TObject);
begin
  //Соединяемся с сервером и посылаем ему введенную команду
  IdTCPClient1.Host := host.Text;
  IdTCPClient1.Port := StrToInt(port.Text);
  IdTCPClient1.Connect;
  IdTCPClient1.Socket.WriteLn(send.Text);
  send.Clear;
  //Ожидаем ответ и закрываем соединение
  try
    ans.Text := IdTCPClient1.Socket.ReadLn; // <-- Строчка на которой подвисает
  except
    ShowMessage('No ans');
  end;
  IdTCPClient1.Disconnect;
end;

end.

using System;
using System.Collections.Generic;
using System.Text;
using System.Net.Sockets;
using System.Net;
using System.Threading;
using System.Text.RegularExpressions;
using System.IO;

namespace HTTPServer {
    class Client {
        private void SendAnswer(TcpClient Client, string Str) {
            Str += "\r\n";
            byte[] Buffer = Encoding.ASCII.GetBytes(Str);
            Client.GetStream().Write(Buffer, 0, Buffer.Length);
            Client.Close();
        }
        public Client(TcpClient Client) {
            string Request = "";
            byte[] Buffer = new byte[1024];
            int Count;
            while ((Count = Client.GetStream().Read(Buffer, 0, Buffer.Length)) > 0) {
                Request += Encoding.ASCII.GetString(Buffer, 0, Count);
                if (Request.IndexOf("\r\n\r\n") >= 0 || Request.Length > 4096) { break; }
            }
            Console.WriteLine(Request);
            string Headers = "Answer\r\n";
            byte[] HeadersBuffer = Encoding.ASCII.GetBytes(Headers);
            Client.GetStream().Write(HeadersBuffer, 0, HeadersBuffer.Length);
            Console.WriteLine("Answer sended");
            Client.Close();
        }
    }

    class Server {
        TcpListener Listener;

        public Server(int Port) {
            Listener = new TcpListener(IPAddress.Any, Port);
            Listener.Start();
            while (true) {
                ThreadPool.QueueUserWorkItem(new WaitCallback(ClientThread), Listener.AcceptTcpClient());
            }
        }
        static void ClientThread(Object StateInfo) {
            new Client((TcpClient)StateInfo);
        }
        ~Server() {
            if (Listener != null) {
                Listener.Stop();
            }
        }
        static void Main(string[] args) {
            int MaxThreadsCount = Environment.ProcessorCount * 4;
            ThreadPool.SetMaxThreads(MaxThreadsCount, MaxThreadsCount);
            ThreadPool.SetMinThreads(2, 2);
            new Server(8000);
        }
    }
}

public Client(TcpClient Client) {
	string Request = "";
	byte[] Buffer = new byte[1024];
	int Count;
// Тут идет считывание от Клиента
	while ((Count = Client.GetStream().Read(Buffer, 0, Buffer.Length)) > 0) {
		Request += Encoding.ASCII.GetString(Buffer, 0, Count);
		if (Request.IndexOf("\r\n\r\n") >= 0 || Request.Length > 4096) { break; }
	}
	Console.WriteLine(Request);
// А тут вроде совершенно независимый ответ
	string Headers = "Answer\r\n";
	byte[] HeadersBuffer = Encoding.ASCII.GetBytes(Headers);
	Client.GetStream().Write(HeadersBuffer, 0, HeadersBuffer.Length);
	Console.WriteLine("Answer sended");
	Client.Close();
}