HomeGroup is really time sensitive, the time on all machines belonging or joining a HomeGroup must be exactly correct and synced. A fraction of a second time difference can mean a PC can't join a HomeGroup.
The below procedure helps surprisingly often to get a computer joined in HomeGroup:
1.) Go to time settings:
2.) Open the additional time settings:
(Click screenshots to enlarge.)
3.) Click the Set the time and date link:
4.) Select the Internet Time tab, click Change settings:
5.) To sync the time, click the Update now button:
6.) Click OK, reboot:
Do this on all the other HomeGroup computers first, then last on the computer having issues in joining the HomeGroup.