I found a way to cope with 'th', 'st', 'nd' and 'rd'. It's not that pretty but if you wrap it up into a function you've got a workable solution. It would be nice if you could just ignore characters, then you could use something like "d##MMMMyyyy" where # would be a character that's ignored. However, I couldn't find anything in the documentation that would lead me to believe that's possible. Anyway here you go.
' Valid date formats
Dim validFormats As String() = {"d'st'MMMMyyyy", "d'nd'MMMMyyyy", "d'rd'MMMMyyyy", "d'th'MMMMyyyy"}
Dim myDate As Date = Date.ParseExact("1stDecember1993", validFormats, Globalization.CultureInfo.CurrentCulture, Globalization.DateTimeStyles.None)
Your original post showed no spaces for the date...it was 7thNovember1993. If that's not the case just add appropriate spaces into the formatting strings and it should work.