I'm using ISPConfig to setup all the websites on my server but I also like to try to fiddle with the files myself to see how it works.
Like you guessed, yes, I've broken something.
I can't access my webmail setup by default on the server with the alias /webmail (I access it via the http://xxx.xxx.xx.xx/webmail)
Firefox tells me that 
  The page isn't redirecting properly
      
Firefox has detected that the server is redirecting the request for this address in a way that will never complete.
So I cleaned up my vhost files and the one of my websites work as intended, I think that the problem comes from my default.vhost.
Here's the content of it
<Directory /var/www/>
    AllowOverride None
    Order Deny,Allow
    Deny from all
</Directory>
<VirtualHost *:80>
DocumentRoot /var/www/
    ServerAdmin 
[email protected]
    <Directory /var/www/>
        Options FollowSymLinks
        AllowOverride All
        Order allow,deny
        Allow from all
</Directory>
</VirtualHost>
This isn't a lot and I can't really see what's wrong with it, all I know is that it isn't the one that came with ISPConfig and I can't find an original one.
Here's the roundcube.conf that loads with apache
# Those aliases do not work properly with several hosts on your apache server
# Uncomment them to use it or adapt them to your configuration
#    Alias /roundcube/program/js/tiny_mce/ /usr/share/tinymce/www/
#    Alias /roundcube /var/lib/roundcube
Alias /webmail /var/lib/roundcube/
# Access to tinymce files
<Directory "/usr/share/tinymce/www/">
      Options Indexes MultiViews FollowSymLinks
      AllowOverride None
      Order allow,deny
      allow from all
</Directory>
<Directory /var/lib/roundcube/>
  Options +FollowSymLinks
  # This is needed to parse /var/lib/roundcube/.htaccess. See its
  # content before setting AllowOverride to None.
  AllowOverride All
  order allow,deny
  allow from all
</Directory>
# Protecting basic directories:
<Directory /var/lib/roundcube/config>
        Options -FollowSymLinks
        AllowOverride None
</Directory>
<Directory /var/lib/roundcube/temp>
        Options -FollowSymLinks
        AllowOverride None
        Order allow,deny
        Deny from all
</Directory>
<Directory /var/lib/roundcube/logs>
        Options -FollowSymLinks
        AllowOverride None
        Order allow,deny
        Deny from all
</Directory>
I didn't touch that file, but I guess it has something to do with the problem.
I just can't find why it doesn't work.
EDIT:
This is the errors in my apache's log
[21/Jun/2013:21:10:54 +0200] "GET /webmail/ HTTP/1.1" 302 540 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:21.0) Gecko/20100101 Firefox/21.0"
[21/Jun/2013:21:10:54 +0200] "GET /webmail/ HTTP/1.1" 302 475 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:21.0) Gecko/20100101 Firefox/21.0"
[21/Jun/2013:21:10:54 +0200] "GET /webmail/ HTTP/1.1" 302 475 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:21.0) Gecko/20100101 Firefox/21.0"
[21/Jun/2013:21:10:54 +0200] "GET /webmail/ HTTP/1.1" 302 475 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:21.0) Gecko/20100101 Firefox/21.0"
[21/Jun/2013:21:10:54 +0200] "GET /webmail/ HTTP/1.1" 302 475 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:21.0) Gecko/20100101 Firefox/21.0"
[21/Jun/2013:21:10:54 +0200] "GET /webmail/ HTTP/1.1" 302 475 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:21.0) Gecko/20100101 Firefox/21.0"
[21/Jun/2013:21:10:54 +0200] "GET /webmail/ HTTP/1.1" 302 475 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:21.0) Gecko/20100101 Firefox/21.0"