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Log in through FTP, and delete any faulty modules as a starter. Log into your site and head ovder to module administration and verify that the modules don't show up on the bottom half of the page.
Upload a module for testing, and see if you get the same results. Try to make this one of the ones that failed on you. As soon as it installs, uninstall it to remove the tables it added to your Database. This is just for kicks at this stage. If it happens to work, your in luck. If not, well, you have to dig a little deeper.
Log into phpmyadmin through your site administration panel, this will either be Plesk or CPanel, depending on your hosting environment.
Back up your database.
Look for and delete any module tables that point to the faulty modules. Don't be afraid to browse around a bit, you won't harm anything. You will more then likely find the offending faulty module installation tables on the first page of your phpmyadmin page.
Check them off, and drop the tables. This will effectively uninstall your module. Go back to your FTP and delete the test module we did above if it's still failing.
Why all this is happening, I can't tell you. This is what I Would do if I were in your shoes and shouldn't take more then 10 or 15 minutes of your time.
Good Luck.
XOOPS Community Support