The number of dots do not reflect the number of characters in the password. This is a security
feature.

SQL Server and Windows logins are different beasts.  With a SQL Server
login, it is SQL Server that maintains and validates the password.  However,
with a Windows login, Windows validates the user identity based on the
current user credential and SQL Server knows only only the account name and
SID (not password).

Below is a sample script grant a Windows account access to SQL Server and a
database.

USE MyDatabase;
CREATE LOGIN [MyDomain\MyAccount] FROM WINDOWS;
CREATE USER [MyDomain\MyAccount];

About the changing the length of the dots of your passwords are about
security as Tibor mentioned. Your password does not change in reality. This
is made only not to show the others the length of your real password.

If your first post, you said that you installed an instance of SQL Server
2005 Express Edition on a PC and you tried to reach it from another PC using
SSMS.

If you do not have a trusted environment or you work in a trusted
environment but you don't have a valid Login for your Actve Directory
account in your remote SQL Server server, then you can't log in to it.

However I somehow believe that your computers are independent, they are not
a part of a trusted environment. They are just in the same workgroup or not
even in the same workgroup. In this case, you still have a chance to connect
to your remote SQL Server instance using Window Authentication by setting up
two same Windows accounts. For example, create a Windows Account on the SQL
Server server with a user name "SQL" and password "xxx". Create this same
Windows Account in your other PC with the same user name and password.
Create a Login for this windows account in your SQL Server. And log in to
your Windows in your second PC using this Windows account then you'll be
able to connect to your SQL Server using Windows Authentication.

However, in SQL Server 2005 Express Edition, remote connection is disabled
by default. You'll need to enable it. If your SQL Server instance is a Named
Instance, then ensure your Browser Service is running and up. Configure your
Firewall to let your SQL Server ports. Ensure you can ping your SQL Server
server from your second PC and vice versa.

In non-trusted environments, it's better using SQL Logins rather than
Windows Authentication.

Also, to create a Windows Login on a stand-alone SQL Server server using the
following code as Dan's given you as a sample:
CREATE LOGIN [data_main\Andrew] FROM WINDOWS;
CREATE USER [data_main\Andrew];

You should format the Login name this way:
"Your_Computer_Name\Your_Existing_Windows_Account"

For example, My computer name is "EKREM-PC" and my user name is "Ekrem" on
my test machine. So, to create a Windows Login, I should execute the
following code:

CREATE LOGIN [EKREM-PC\EKREM] FROM WINDOWS;
CREATE USER [EKREM-PC\EKREM];