I'd recommend using a regular expressions instead of string operations for this:
Set fso = CreateObject("Scripting.FileSystemObject")
filename = "C:\VBS\filediprova.txt"
newtext = vbLf & "<tr><td><a href=""..."">Beginning_of_DD_TC5</a></td></tr>"
Set re = New RegExp
re.Pattern = "(\n.*?Test Case \d)"
re.Global = False
re.IgnoreCase = True
text = f.OpenTextFile(filename).ReadAll
f.OpenTextFile(filename, 2).Write re.Replace(text, newText & "$1")
The regular expression will match a line feed (\n) followed by a line containing the string Test Case followed by a number (\d), and the replacement will prepend that with the text you want to insert (variable newtext). Setting re.Global = False makes the replacement stop after the first match.
If the line breaks in your text file are encoded as CR-LF (carriage return + line feed) you'll have to change \n into \r\n and vbLf into vbCrLf.
If you have to modify several text files, you could do it in a loop like this:
For Each f In fso.GetFolder("C:\VBS").Files
If LCase(fso.GetExtensionName(f.Name)) = "txt" Then
text = f.OpenAsTextStream.ReadAll
f.OpenAsTextStream(2).Write re.Replace(text, newText & "$1")
End If
Next