5
Using Groups rights for the same thing as mentioned works for me. Some things to try are to go into each core group and hit Update. Sometimes this shakes up problems in the Admin area.
Remember that in a new Group you don't have to check off everything, just the areas that aren't already included in other groups that user is also a member of (like "registered users"). This will save you lots of work later on. In my case I have blocks that I only want anonymous to see and I don't want to uncheck a million lines in other groups to do it.
If you give Admin rights for a select group of modules to a group then those users should see the Administration link in their User menu.
Also, list all versions being used if you still have trouble.