The best thing England can do is not panic. No cute selections or changing half the side. England need a win here (or at least two draws), and that means playing the best side possible. I agree with PEWS that a spell for Broad will be best if he isn't 100% because you don't want to make his injury even worse, but other than that no changes unless you're sure Ballance, Rankin or whoever is a better player than the guy you drop. As Ausage said, it's very easy to drop half the team and then hide behind the rebuilding tag for half a decade or more of mediocre performances.
Bad series happen. England are at the end of a long period of cricket and the break after this will be good for the players (and angry fans) to get away from the game, calm down and start again in a few months.
edit: it's not as though you don't have youth in the team anyway. Root and Stokes are there, and both have shown signs they will be good players for years to come.
edit2: the more you look at it, the more you can't help but just shrug your shoulders from an English perspective. How likely was it that Harris would stay on the park for multiple tests, Watson would do the same and Johnson would string three world class bowling performances together? Not likely. On top of it you have to contend with a keeper batsman in career best form and a man well in contention for the title of the best batsman in the world.
Then you put that against a team with an opening batsman who has been outplanned and is in poor nick to boot, a number three who had to pull out, an offie in Australia and Prior and Anderson out of form and it's a recipe for something like this.
The stars have aligned for Australia really, and because they have a team containing many good and world class players they have taken the chance to hammer the oppo. At least you won't have to face some of these blokes next time around.