I found the problem. It appears that this appSetting element was still in my Web.config from earlier releases of Sitefinity even after the upgrade to Sitefinity v. 8.1.5800:
<add key="servicestack:license" value="1219-e1JlZjoxMjE5LE5hbWU6VGVsZXJpayBBRCxUeXBlOkJ1c2luZXNzLEhhc2g6aU84Yld6emt2UG9tN2xNOFBONWpqRmtsNElvZjVFQWxRTCtZVGI2VTZSUHBMbnRVd2xISnhWeTgvQWJJazJPa1BLMDFWZ2FnRUMzZHcyVG1laFhUaTd1MndYUGVLb2pNWUE5NEdyMHVYNUxpUkNmckxWcUFMTytQWFJtN1E0N1hMYXMrbzdweTJZTk52eGRzbkN0Rkd3eWpNeUFmaXB1b2J0Q1kyUkJUNTE0PSxFeHBpcnk6MjAxNS0wMi0xNX0=" />
Once I removed this element, Sitefinity rendered correctly.
I just upgraded my site to Sitefinity v. 8.1.5800 and I am now getting a ServiceStack License expiration error message.
I have attached a screenshot of the error message.