There is no way at all to accomplish this, just as there is not on the television, the televsion requires the mass cooperation of all the broadcasters to pull it off as well. Furthermore, the internet works in a interesting way, and there are many technologies that run on top of it that each need to be addressed.
First, there is the operating system itslef, this would be the best place to attempt to implement this, and to the best of my knowledge, could be done now. Both Macintosh and windows now offer automatic notification of OS updates, this being a message the OS company puts out based on the current version you are running. So all they would have to do is just reconfigure things so that rather than “the monolith has patched a previous security hole, you should update it” poppin up, you would get the Eneergnecy message.
Next, are the many serives that run ontop of the internet.
http web browser, to the best of my knowledge, the browser itself does nothing on it’s own, it is a send recieve communication, you send a request, the computer on the other end gets it, and sends something back. So on its own, there is not much to be done about this. There are a few roundabout ways. Most browsers default to a certain page when you launch it, so it would not be too hard to get a list of all browsers default pages and put up some message at those sites, again, this would not get the whole world in one shot either. The previous idea of redirecting all traffic to one site, as posted earlier, would probably just crash the server on the other end. No amount of server farming, load balancing etc could deal with a hit that large IMO, or at least the cost of such a system would make it prohibitive for such a one time use.
The next means being email, first I want to discount the email forwarding scheme that is mentioned above. Most savy internet users know to regard forwards as fake or hoaxes, and I would not want something serious like a Emergency Broadcast Message to be confused as for it’s validity. You would also be very surprised of the sheer vastness of email servers out there, I run a few myself, and not all of them are capable of broadcasting a message to all users. Granted, AOL, yahoo, hotmail, etc, places like that certainly can, but smaller ISP’s like the local ones most use to dial into, would have a hard time doing this, and I can say for certain, several of the mail servers I run can not do such a think without taking steps to make this happen early on in the configuring of the server.
Now on to Instant Messsaging, this being the one way that is opposite of send and wait for a receive, they can indeed pump out a message at will like that. However, the infrastructure behind this is even less robust than that of webservers. I have seen AIM chat rooms as small as 50 people crash all the time, and the service is far from reliable.
The bottom line, I would not even want this to happen, too much trouble to implement a system that is used in such rareness and could be abused in such mass. As it is now, I can not jump through more than 3 sites without getting some update here or there on one site.
Also, as far as I know, every town has loud horns that sound off in the event of a emergency, or at least a neighboring town that you could hear it from, which will tell you to turn the radio or television on