OK, so the username is the same on both machines: billp
Then, assuming the password is the same also (and I think it will be), try @CrystalGipsy 's suggestion of creating a local user (name: roon) on your new laptop, and add it to the Network Folder sharing permissions…
Well done for persevering. Thought it might be the issue. They seemed to change the security levels for shared access some time ago. It drove me to distraction as my own login just refused to work. Sometimes they make it ridiculously hard to achieve what should be a simple task.