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jenclas, thanks for your help.
I've tried several things before posting again, but I still cannot login, either as admin or a normal user (and it's the same for the users of my website, so, it's not a firewall problem or something like that).
About the blank page, I don't get a blank page. I log in normally, it says I'm logged then, come back to the homepage, but I'm not logged. I've tried to go directly to the admin page after login, but it failed too.
I've tried to repair the database, but nothing change.
Also, even if I can login by a way or another, I'm wondering if visitors will be able to login...
I'd like to be able to login to, at least, write a message to say "sorry" for this problem...
I was wondering what I'd have to change in the database to change the state to "logged".
I've also noticed that sessions tables are different between my two websites (I mean there are 11 fields for the site I cannot login, and maybe 4 on the other I can log). I don't really know why anyway...
Thanks in advance for your reply.