I want to tell WPF: \"If TextBlock contains no data, then don\'t show it.\"
TRY #1 with a simple trigger produces
Either Try #2 or Try #3 should be fine - the problem is in the line where you are referencing the style - you need to use either 'Style="{StaticResource [KeyName]}"' or 'Style="{DynamicResource [KeyName]}"'.
Try this (in Try #2):
In Try 1 you reveal a limitation of current WPF versions: Triggers are not supported directly on elements.