After you have set you block to 'visible' in admin>blocks settings:-
1- make a note of the name of your custom block title.
2- Go to sytem admin>groups>edit groups registered users
3- Find your custom block and make sure it has a check mark
4- Update the group
5- return to groups main page
6- select edit groups> anonymous users
7- Find your custom block again
8- Make sure there is a check mark against it as before.
9- update the group.
10 -repeat for any other groups you wish to see the block
The same procedure is common to all blocks wether custom or part of a module.
NOTE: some module have a built in blocks setting page for positions and group permissions. This simply duplicates the system blocks setting page ans groups permissions pages.
It's always a good idea to check both, to be sure
Please also see Flash tutorial:Basic admin configuration and First website content.