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In your case, it's probably a good idea to install XOOPS to a subfolder. The webserver might get confused what to serve, index.html or index.php. That's something that has to be configured on the server, or with htaccess. In any case, under normal circumstances, you should get either your old homepage, or the XOOPS frontpage.
Now, what's strange is that redirection to some placeholder from what seems to be your webhost if you try to hit directly on the index.php. If your XOOPS were installed correctly, you should be able to access it at yourdomain/index.php. Also, index.html or index.htm are not present or accessible it seems.
There may be an issue with file permissions set on the server. If, for instance, you've played around with permissions for the webroot folder and made it non-executable and/or non-readable for the world, then that might explain something. You could try to undo all the changes in permissions you've made if you remember them. 755 is a good choice for the webroot, assuming that your site is hosted on a Linux/Unix box. That would be read/write/execute access for the server, and read/execute for everyone else.
Also try removing or renaming all .htaccess files that might apply to your webroot. Those would be those that are at your root level and at /htdocs or /public_html. You should, of course, back them up and go through them to see what are the settings you would want to restore afterwards.
Finally, if the thing worked at some point but stopped without you doing anything, you should get in touch with support at your webhost. There may have been some hack attack, or they've just screwed something up big time.
In any case: If you install XOOPS over a working site (something with index.html) and install it correctly, then the two things shouldn't interfere I believe. Only that the webserver would make a choice what to serve up. Your static index.html, or Xoops's index.php.
