I just tried to add a statcounter to my blog. Support says that you can add a statcounter using the widgets, but there is no statcounter widget. So I tried using a textbox, and now the textbox 2 is in top of another widget and none of the widgets can be moved; furthermore, the layout of my blog has been affected.
What browser are you using? If you are using Safari on a Mac, this is a known problem as Safari can’t handle some of the java they use here at WordPress. I switched to Firefox for working on my blog and it works fine.
Do you have an account set up at statcounter yet? When you set it up they will display the HTML code you need to put into the text widget. Copy that code and paste it into the text widget. The little lined icon on the right side of the widget will open it up so you can insert the code.