sendMessage from extension background or popup to content script doesn’t work

In your background page you should call

chrome.tabs.query({active: true, currentWindow: true}, function(tabs){
    chrome.tabs.sendMessage(tabs[0].id, {action: "open_dialog_box"}, function(response) {});  
});

instead of using chrome.extension.sendMessage as you currently do.

The chrome.tabs variant sends messages to content scripts, whereas the chrome.extension function sends messages to all other extension components.