+2  A: 

Is the DocumentViewModelList a property of your DocumentViewModel?

Typically, what I would have is a ViewModel for that window which would expose an ObservableCollection<T> where T is what you want displayed in the list. Then, you can assign the Window/Page/etc.'s DataContext to the ViewModel, and then bind the ItemsSource of the ListBox to that ObservableCollection<T> property.

For example, here would be a snippet of my ViewModel.

public class SomeViewModel
{
  public ObservableCollection<SingleDocumentViewModel> Docs {get; private set; }

  // other properties can go here
}

In the code-behind for the XAML, (I usually do it in the constructor), you can set its DataContext to a new instance of your ViewModel

public AwesomeDocumentList()
{
  this.DataContext = new SomeViewModel();
  // the rest of the constructor
}

With the Window's DataContext set, you can bind the ItemsSource to the exposed property (I called it Docs)

<ListBox ItemsSource="{Binding Docs}" ... />

Hope that helps.

Update

In the RelayCommand for the button, do you have something specified for the CanExecute predicate? If not, then I believe the RelayCommand will default to always enabled. But if you have a predicate specified, take a look in there.

The code you posted for the IsSelected property looks fine. Looks like the problem lies elsewhere.

Eric
please read again Eric, I have updated the question :)
Lisa
I have updated the init thread Eric!
Lisa
@Lisa Eric's solution is absolutely correct. If you are having so much trouble doing what you want to do, there is a problem in the way you have set up the ViewModel. Try simplifyling everything and start from scratch. You'll quickly find the problem.
NVM
@For the first solution I helped myself. And his 2nd solution is no help. My ViewModels are setup correctly. My problem could something have to do with this: http://social.msdn.microsoft.com/Forums/en-US/wpf/thread/a2394616-9cbf-400d-b632-284cc56a2666 but I tried all the suggestions and nothing helped. I will open a new thread @Eric Due to your help I accept your solution although I was faster ;P am too busy to write a solution answer now...
Lisa
@NVM if you think I have setup something wrongly, check this out! => http://stackoverflow.com/questions/3695719/isselected-property-of-viewmodel-bound-to-listbox-only-first-item-selection-work
Lisa