On the laptop, both of us (as we have tried with both accounts) will sign in and that will be successful. However, after we sign in successfully, the character screen pops up - but not our already created characters. We have to start from scratch and are not connected to RealId. We are also getting a message saying something along the lines of our account not being a valid Diablo account, regardless of the fact that we can play it on the desktop sitting beside the laptop and the desktop at my own home.
We've restarted the router, restarted the laptop, signed in under each account and nothing is working. All we can do on the laptop is start fresh, only to have it be deleted as soon as we log out.