You can retreive all the components from your panel with getComponents() (it returns all components as Component array). Iterate through array with a loop and disable each component.
JTextArea is a specific component in this case. Actually, when you have it on your panel, what you get is not the text area, but scroll pane (automatically added when you add text area). So what you should actually do is implement a recursive method, that can pick those components that are "deeper" (like the case here). Once you have them all (e.g. in a list), disable all of them.
The quieter you are, the more you are able to hear.
I presume this is the old thread you mentioned. I haven’t read it. Did it discuss the enable() and disable() methods? You are not supposed to use them any more; use setEnabled(true) or setEnabled(false). It is worth going through the hierarchy of Swing components and finding how many have setEnabled() methods at all; I can’t remember where that method is declared.