Hi, I'm sure this will help many of you as I was getting exactly the same problems as a lot of you.
Firstly, I decided to address the problem when my computer was constantly resetting itself and the problem seemed to be getting more frequent.
So, I checked my event log (Computer(rightclick) > Manage > Event Viewer > Windows Logs > System). It showed me a whole bunch of errors containing two services. Either Peer Networking Grouping or Peer Name Resolution Protocol. I checked out Services (type services in the search bar on start) and found that I could not start these two services manually either. I disabled them which stopped my computer restarting itself and cleared the event log of any errors I was receiving before.
I now, however, couldn't see any other computers in my Homegroup and couldn't leave it, change what I was sharing or view the password, which are many of the symptoms you guys were receiving.
How I fixed the problem
Go to C:\Windows\ServiceProfiles\LocalService\AppData\Roaming\PeerNetworking and delete all of the files in this folder. Now restart the computer.
Go to Services again and you should be able to start 'Peer Networking Grouping' and 'Peer Name Resolution Protocol'. Restart the computer again.
When you log on this time, check the event log again, to ensure no errors concerning the two services are present and also check Services to ensure the two services concerned are running.
You should now have full functionality restored to your homegroup.
I hope this helps, let me know if it works.