Cannot get any tweets using Twitter Block
Have you tried using the twitter profile widget? The twitter profile widget allows you to stream a twitter feed from a specific user. 


First you will need to log into twitter and configure a twitter widget. When you configure  the twitter widget (using your twitter account) you will have output html code. 
Once you do this you can then create a content type called twitter widget. Once this content type is created all you have to do is place the html text from your twitter widget into the content type. 
Make sure that in your content type text box you set the text to read plain html. Once saved this will create block that can then be configured and dragged around the page.