I also have a copy of FMP 10, I opened the same database there and it worked, so I know it's not the file.
Actually, it still could be the file. Sometimes hidden damage in a file produces issues with one release of filemaker and not another.
Try creating a small test file and see if you can open the Manage Layouts window in it.
I just tried that and it still does not show up.
There isn't any system setting that controls this to my knowledge. It should be always available if you have the file open with a full access password or if the database does not have a password defined.
What operating system do you have? If it is Mac, you might try trashing preferences for this file.
Otherwise, I think you'll need to see if re-installing FileMaker fixes the problem.
I am on a mac - I tried deleting the preferences file in user>library>preferences. No luck - do you know of other preferences files to also delete? I'll try the reinstall if that doesn't work