When you first created your Homegroup, Windows would have made you pick a password for it. I would assume you set up the Homegroup on your desktop. So, why not just "change" the password there for the Homegroup? I'll put the instructions here, but there's a nice video at the link.
To change a homegroup password
Open HomeGroup by clicking the Start button, clicking Control Panel, typing homegroup in the search box, and then clicking HomeGroup.
Click Change the password, and then click Change the password.
Type the new password you want to use (or accept the suggested one), click Next, and then click Finish.
At that point, you should have no issues connecting to your Homegroup, and accessing your designated shared/public directories.