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Hi,
What you would need to do is make the block visible. Then go into groups admin, and check the blocks that members of each group can view.
That should work, but it sounds like you're doing that, so I'm not sure what the problem might be.
Cheers,
Dee
PS Just thinking about it, sometimes groups such as registered members, by default get access rights to blocks, so might need to uncheck their access. I tried playing with my blocks, and I didn't have any problem with changing which groups can view it.