First try logging out of your site's administrator area. When you are logged in the secret URL parameter check doesn't run, of course. Then try accessing your site's back-end using the old secret URL parameter, e.g. http://www.example.com/administrator?test where www.example.com is your site and test is your old secret URL parameter.
If this doesn't redirect you to the main page of your site (front-end) please try doing the same from a different computer connected to the Internet through a different ISP so as to make sure that your IP is different. Yes, I know what you wrote, but I'd like you to check this anyway.
If this doesn't redirect you to the main page of your site (front-end) go to your site's back-end, Extensions, Manage Plugins and find the System - Admin Tools plugin. Make sure it's enabled and that the Access is set to Public. Guest, blank or any other setting will NOT work.
If this is not the case, go to your site's back-end and click on Site, System Information, then click on the PHP Information tab. The PHP version listed there should be at least 5.3.1. If it's an earlier version Admin Tools will not work.
If this wasn't the case, try re-installing Admin Tools because you seem to be missing some files from the Admin Tools plugin.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
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