After installing, if I enter the member area of my site (a section visible only to registered users), it only shows a blank page.
Do you mean site frontend?
I need more detailed information about used 3rd pary extensions. Last time we've blank page was conflict with CSS2SWITCH plugin. So you could have also conflict with some 3rd party extension.
Could you check Apache's error log on your server? It could contain detailed information about error.