Hi, friend really your problem and look seriously and need to do an analysis on your server and the code of your site to check where the bug is (lack of security) that is enabling people (defacer, kides script) and not take your hacker site of the air after this step out ai yes you can put your site noar again, because if we do not resolve this and put your site in the air again, you probably suffer a new attack.
Well I pass the version of your Joomla, Mysql (database) and the server if Apache or another, so I try here and even help you diagnose your problem!