So, i'm trying to login to login to Technic Launcher for the first time on a pretty new PC, just a week after migrating my account and changing my name. It refuses to work. I have tried E-Mail, username, my old username, even older passwords. All combinations, and they refuse to work.
When I had that problem, it was because I was using my old Minecraft username instead of my email address after creating a Mojang account and linking my Minecraft username to it.
Go log in at Minecraft.net. If that works, use the exact same name/email and password to log in from the Technic Launcher. If it doesn't work, hit that "Forgot Password" link and reset your password at minecraft.net. Then use the new name/email and password at the Technic Launcher.