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Regarding your site being sluggish, there are some items within the wiki and within these forums that will help you speed up your website.
Xoops does allow the user to cache a lot of the site from the admin area. Also I would empty the cache folder now and then to stop the cache folder getting to large.
As for your the blank page, there is two ways you can find out the reason for this, one, look through your php error log for any errors at the time they said they tried to log in and see if you can find anything related to this.
Or, you could enable php error reporting within the site and ask the user to report any errors that it may show.
Without some sort of error report from yourself here at this forum, there isn't really much we can do to debug this situation and I don't think stabbing in the dark with produce much either at this point. :)