Ajuda - Não consigo executar a aplicação pelo Tomcat do Eclipse

[dadivajah]

Boa noite pessoal,

Sou novo tanto aqui no forum quanto em Java, estou encontrando certas dificuldades em implementar meu TCC, estou montando um portal sobre Lógica de Programação, onde o mesmo contém um BD p/cadastro, login e senha (usando Filters) e outras coisinhas mais.

Se possível gostaria que vcs dessem uma olhada no meu código e ver se o mesmo está ok. Estou grandes dúvidas em relação a classe Filtro, pois é atráves dessa classe que eu restrinjo o acesso as outras páginas do site, caso o usuário tente acessar diretamente pela url.

A estrutura do projeto está da seguinte maneira:

Nome do Projeto
WEB-INF: (contém as demais paginas do site (separadas por pastas) e a página logado.jsp (dentro do WEB-INF) e as libs.
Web-Content: contém a index.jsp (caso o usuário efetue o login corretamente ele deveria ser redirecionado para a página logado.jsp, conforme descrito acima.

Desde já agradeço!

package com.cadastro;

import java.io.IOException;
import java.io.PrintWriter;
import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.PreparedStatement;
import java.sql.ResultSet;

import javax.servlet.ServletException;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;

public class Cadastro extends HttpServlet {

	private static final long serialVersionUID = 1L;
	private String nome;
	private String email;
	private String login;
	private String senha;

	Connection con = null;
	PreparedStatement stmt = null;
	ResultSet rs = null;

	public Cadastro() {
	}

	public String getNome() {
		return nome;
	}

	public void setNome(String nome) {
		this.nome = nome;
	}

	public String getEmail() {
		return email;
	}

	public void setEmail(String email) {
		this.email = email;
	}

	public String getLogin() {
		return login;
	}

	public void setLogin(String login) {
		this.login = login;
	}

	public String getSenha() {
		return senha;
	}

	public void setSenha(String senha) {
		this.senha = senha;
	}

	protected void doPost(HttpServletRequest request,
			HttpServletResponse response) throws IOException, ServletException {

		response.setContentType("text/html;charset=UTF-8");

		PrintWriter out = response.getWriter();
		String nome = request.getParameter("nome");
		String email = request.getParameter("email");
		String login = request.getParameter("login");
		String senha = request.getParameter("senha");
		String senha2 = request.getParameter("senha2");

		if (senha.equals(senha2)) {
			try {
				Class.forName("com.mysql.jdbc.Driver");
				con = DriverManager.getConnection(
						"jdbc:mysql://localhost/e_learning", "root", "root");
				stmt = con
						.prepareStatement("insert into cadastro (nome,email,login,senha)values(?,?,?,?)");
				stmt.setString(1, nome);
				stmt.setString(2, email);
				stmt.setString(3, login);
				stmt.setString(4, senha);
				stmt.execute();
				stmt.close();

				response.sendRedirect("index.jsp");
			} catch (Exception e) {
				out.print(e.getMessage());
			}
		}
	}

package com.filtro;

import java.io.IOException;

import javax.servlet.Filter;
import javax.servlet.FilterChain;
import javax.servlet.FilterConfig;
import javax.servlet.RequestDispatcher;
import javax.servlet.ServletException;
import javax.servlet.ServletRequest;
import javax.servlet.ServletResponse;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpSession;

import org.apache.commons.lang.StringUtils;

import com.login.Login;

public class Filtro implements Filter {

	String page = "index.jsp";

	public void init(FilterConfig filterConfig) throws ServletException {
		if (filterConfig.getInitParameter("page") != null) {
			page = filterConfig.getInitParameter("page");
		}
	}

	public void doFilter(ServletRequest req, ServletResponse response,
			FilterChain chain) throws IOException, ServletException {

		HttpServletRequest request = (HttpServletRequest) req;
		HttpSession session = request.getSession();

		Login login = (Login) session.getAttribute("login");
		RequestDispatcher dispatcher = null;

		if (login == null) {
			dispatcher = req.getRequestDispatcher("index.jsp");
		} else {
			// dispatcher = req.getRequestDispatcher(request.getRequestURI());
			dispatcher = req.getRequestDispatcher(StringUtils.removeStart(
					request.getRequestURI(), "WEB-INF/pages/logado.jsp"));
		}

		dispatcher.forward(req, response);
	}

	public void destroy() {
	}

}

package com.login;

import java.io.IOException;
import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.PreparedStatement;
import java.sql.ResultSet;
import java.sql.SQLException;

import javax.faces.context.FacesContext;
import javax.servlet.ServletException;
import javax.servlet.ServletResponse;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
import javax.servlet.http.HttpSession;

public class Login extends HttpServlet {

	private static final long serialVersionUID = 1L;
	private String login;
	private String senha;

	Connection con = null;
	PreparedStatement stmt = null;
	ResultSet rs = null;

	public Login() {
	}

	public String getLogin() {
		return login;
	}

	public void setLogin(String login) {
		this.login = login;
	}

	public String getSenha() {
		return senha;
	}

	public void setSenha(String senha) {
		this.senha = senha;
	}

	protected void doPost(HttpServletRequest request,
			HttpServletResponse response) throws ServletException, IOException {
		response.setContentType("text/html;charset=UTF-8");

		try {

			String login = request.getParameter("login");
			String senha = request.getParameter("senha");

			Class.forName("com.mysql.jdbc.Driver");
			con = DriverManager.getConnection(
					"jdbc:mysql://localhost/e_learning", "root", "root");
			stmt = con
					.prepareStatement("select login,senha from cadastro where login=? and senha=?");
			stmt.setString(1, login);
			stmt.setString(2, senha);
			rs = stmt.executeQuery();

			if (rs.next()) {
				HttpSession session = (HttpSession) FacesContext
						.getCurrentInstance().getExternalContext().getSession(
								false);
				session.setAttribute("login", login);
				response.sendRedirect("pages/logado.jsp");
			} else {
				response.sendRedirect("index.jsp");
			}
		} catch (ClassNotFoundException e) {
			e.printStackTrace();
		} catch (SQLException e) {
			e.printStackTrace();
		} finally {
			try {
				rs.close();
				stmt.close();
				con.close();
			} catch (Exception e) {
				e.printStackTrace();
			}
		}
	}

	public void logout() {
		HttpSession session = null; 
		((ServletResponse) session).reset();
	}

}

Web.xml

<?xml version="1.0" encoding="UTF-8"?>
<web-app id="WebApp_ID" version="2.4"
	xmlns="http://java.sun.com/xml/ns/j2ee"
	xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
	xsi:schemaLocation="http://java.sun.com/xml/ns/j2ee http://java.sun.com/xml/ns/j2ee/web-app_2_4.xsd">
	<display-name>E_Learning</display-name>
	<servlet>
		<servlet-name>Faces Servlet</servlet-name>
		<servlet-class>javax.faces.webapp.FacesServlet</servlet-class>
		<load-on-startup>1</load-on-startup>
	</servlet>

	<servlet>
		<servlet-name>Cadastro</servlet-name>
		<servlet-class>com.cadastro.Cadastro</servlet-class>
	</servlet>

	<servlet>
		<servlet-name>Login</servlet-name>
		<servlet-class>com.login.Login</servlet-class>
	</servlet>


	<servlet-mapping>
		<servlet-name>Faces Servlet</servlet-name>
		<url-pattern>/faces/*</url-pattern>
	</servlet-mapping>

	<servlet-mapping>
		<servlet-name>Cadastro</servlet-name>
		<url-pattern>/Cadastro</url-pattern>
	</servlet-mapping>

	<servlet-mapping>
		<servlet-name>Login</servlet-name>
		<url-pattern>/Login</url-pattern>
	</servlet-mapping>

	<session-config>
		<session-timeout>10</session-timeout>
	</session-config>

	<listener>
		<listener-class>
			org.apache.myfaces.webapp.StartupServletContextListener
		</listener-class>
	</listener>

	<welcome-file-list>
		<welcome-file>index.jsp</welcome-file>
	</welcome-file-list>

	<filter>
		<filter-name>Filtro</filter-name>
		<filter-class>com.filtro.Filtro</filter-class>
	</filter>
	<filter-mapping>
		<filter-name>Filtro</filter-name>
		<url-pattern>/faces/*</url-pattern>
	</filter-mapping>


</web-app>