The other computers aren't asking for credentials at all, just saying they don't have permission.
Sounds like HomeGroup services are trying to negotiate credentials.
Go to control panel's Network and Sharing Center.
Make sure your network is set as a "private network" on all PCs.
Then on the left hand side go to "Change advanced sharing settings".
For "Private (current profile)" make sure everything is enabled. Under homegroup settings, set the option to "use user accounts and passwords to connect to other computers".
Then open my computer (or any explorer window) and type this in the address bar:
\\name-of-remote-computer\c$
you should get a username & password prompt. Enter username in the following format:
name-of-remote-computer\remote-admin-user-name (example if the computer's name is johns-pc and the username is john, enter johns-pc\john as the username.)
enter usual password for that account.
If you still don't get a password prompt you can try deleting your credentials for the remote computer. In control panel, find Credential Manager. Look for the remote computer in the list and delete any saved credentials relating to it.