Sorry the simple solution was not for you.
I use qTranslate for multilingual features and with its help multilingual home page is possible - but not perfect.
I have managed to get all text in the central part (headline over image and the button text part) to show up in a choosen language. For this I have used the qTranslate syntax
<!--:en-->english text<!--:--><!--:se-->svensk text<!--:-->. The drawback is that once entered and saved in the themes option page, the notation disappears from the optionspage but the on the home page correct language text is shown.
For widgets in the widget area, content language is handled by the widget, so you have to pick widgets with proper language support with qTranslate. E.g. the text widget gives correct content but the title is incorrect (all languages shown). In the wdget plugin "Latest News" I get both content and title in correct language (if the posts fetched are in correct language).
Putting up a qTranslate language chooser widget on the home page also allows me to simply switch between languages.
I am a bit confused as to how the webbrowser language preferences actually influences the language of the page (it should, but I'm not sure it works).
Hopes this gives you an idea of what can be done.