I was having the same failed to send message and I found out what happened.
Evidently the 3.6 upgrade took out the mailing information from my contact form.
If you go to your individual Contact Form admin and you look below the form area where is says Mail - message body,to:, From:, Subject:.
All of those fields were blank.
Once I entered in the information the mail form worked.
And if you don't remember of how those fields need to be formatted you can just create a new Untitled form and cut and paste from what was created there.
hope this helps.