You should not need the other classes to do your test - I suggest that you mock them. Mockito is what I would choose, and this question has a nice discussion about various options. If you cannot do your testing by mocking other dependencies, I seriously suggest that you refactor your code, so that it can be done.
If you really do not want to go that (right) path, you could try some dependency injection framework like Spring, and have a separate context for each of your test classes. At junit4 you can use @BeforeClass
@BeforeClass
public void initSpring()
{
Application context = getTestAppContext();//should be unique config for this class
requiredProperty = contex.getBean("someProperty");
}