That won't do it, as the password is asked before Windows even starts, so there is on chance on using a network.
Just a normal LAN connection, teamviewer. It doesn't connect until login anymore.
Ok, Teamviewer, now that's a different thing.
As far as I remember, when installing it gives the chance to install itself as a service (or just as a setting, I have to check this), precisely for this scenario. Have a look at the system services and make sure there is a Teamviewer service set to automatic, and that it's effectively started.
Otherwise reinstalling Teamviewer might help.