OK, I will try again, although I do not think I can help.
Please answer these questions. Do not restate your original problem, since that does not help.
When you open Network and sharing center and click the "joined" link, does the "Change Home Group Settings" window open? there is no join link
If so, what do you see when you click on "Leave the Homegroup"? You should get a window with three options. From what you seem to be saying, if you click on "Leave the homegroup", you get an error stating you cannot leave the group, is that correct?
it says unable to remove the computer from the homegroup.
Have you made sure you have left the homegroup on the laptop? cant leave it.
Have you run the Homegroup troubleshooter?