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Most XOOPS versions apart from the latest do not default to adding checkmarks to the "System Admin" rights in the webmasters group. You don't need to make any changes, just click "update" without filling in the checkmarks and your system admin rights will vanish--this is a common problem.
This no checkmarks thing is fixed in the latest version I understand. I see you have recently moved your site and upgraded from another version? Looks like your "groups" system is operating the "old no checkmarks way" despite your upgrade.
The given solution in stewedo's post is the fix, and it worked for all the others who had the same problem. The "file not found" error looks like a path problem to me. The above path is searching for "admin.php" in your modules/system folder.
You could check the admin.php in your modules/system folder is not corrupted, and no files/folders are missing in the system folder--check the "groups" folder for example.
Paths are defined in mainfile.php in the root of Xoops, check for no trailing slashes etc (you may know this already)