You initialized the Intent wrong way,try this. MainActivity is login screen and HomeActivity is where users gets when login is successful.
if(password.equals(storedPassword))
{
Toast.makeText(HomeActivity.this, "Congrats: Login Successfull", Toast.LENGTH_LONG).show();
Intent intentLetterChecker=new Intent(MainActivity.this,HomeActivity.class);
startActivity(intentLetterChecker);
}