Edit: Try disabling the Guest Account, or removing it's password. There appears to be a permissions conflict if the Guest Account is enabled and PW protected.
I had a similar issue when using a Windows 7 copy that turned out to be fake. My issues started when MS started viewing the product key as deactivated. They eventually gave me a new product key, because it was purchased from a "legit" dealer, who was selling copies with his own enterprise key, and charging retail prices.
It's unlikely that you have the same activation issue I did, but the Network settings described below are a likely culprit.
Long story short, the Homegroup functions are somehow tied to activation, so if you run the MS Genuine Software verification program, and it says it can't activate, it could be related there.
As in your case, everything else worked for me, but the Homegroup and sharing functions never did. You should also check if your network is set on Public. That will cause the same issues, and if you have the same issue I did, you will not be able to change it to Home or Work settings. Public network setting also invalidates the no password sharing, and Homegroup functions.
You can change the Network location as follows:
To change a network location type
If your computer is part of a domain, you won't be able to change the network location type because it is controlled by your network administrator.
Log on to the network.
Open Network and Sharing Center by clicking the Start button , clicking Control Panel, clicking Network and Internet, and then clicking Network and Sharing Center.
Click Customize, and then click either Public (for "Public place" networks) or Private (for "Home" or "Work" networks). If you are prompted for an administrator password or confirmation, type the password or provide confirmation.
Click Next, and then click Close.
Choosing "Private" permanently changes the firewall configuration to allow communication. This can be a security risk.