The Username and Password fields are always grayed out when connecting with
Windows Authentication. After all, Windows knows who you are and has already
authenticated you. And no, you can't change your Windows credentials at this
point.
If the DC computer and your VA computer are in the same domain or in trusted
domains, then your VA computer has already authenticated you and you should
be able to connect.
If you need to connect using a different set of domain credentials, then log
off (in VA), and log back into Windows with those credentials. Or, use the
Run as option in Windows, to start SSMSE with the desired domain
credentials. If you can't do one of these two things, (probably because the
VA computer isn't trusted in the DC computer domain), then you will not be
able to use Windows Authentication.
So then you need to set up SQL Server Authentication on the DC computer.
This may or may not be allowed depending on their policy. Then, in VA, you
can start SSMSE, select SQL Server Authentication, and then provide a user
and password.
All this assumes that the computer DC computer is listening on the internet
is some way. In other words, can you ping the IP address of the DC computer
from VA?
I hope this helps.