Since you're connecting to other Vanilla Private Servers. I'm wondering if it's not catching your attempt to change which server it connects to or using a different client version. It should say 1.12.1 (5875) on the bottom left of the WoW Client.
Here's what you could try - Download and install using the
Nostalrius Installer. Install to C:\World of Warcraft Classic\ do not install into Program Files. Do not modify the realmlist, it's already preconfigured. Run the C:\World of Warcraft Classic\WoW.exe file and try to login.
This is a complete guess but it may be that the username or password is too long or using certain characters that the login server doesn't recognize. You could try creating a simple short test account if you think this may be a possible cause.