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I've been thinking about your issue, and the more I think about it, the more I wonder if you didn't upload a module into the main XOOPS directory, rather than into the modules directory. In that case, the module index.php would have overwritten the root XOOPS index.php, the admin directory for the module would have overwritten the admin directory that is included with the core files, etc. I am not recommending this, but if it were me, I'd reupload the XOOPS core. But, if you did that and it messed up worse, it would not be my fault (disclaimer notice).
I know you're concerned about being hacked, and about getting your site working. But, for future information, please try make one post rather than three when you ask for help. At one point you had three posts on the front page - one was sufficient, IMHO. Hope you get it working soon.
MMM...It tastes like chicken! ...