A few things.
One you'll need to verify that the user you created has the ability to log on. Check the properties inside Sql Server Management Studio. To do this, connect to the database in SSMS. Then find the Security folder. Expand it, and expand the Logins folder. Find the login you are trying to use, right click and choose properties.
On the left is a tree "General", "Server Roles", "User Mapping", "Securables" and "Status". In status make sure that "Permission to connect to database engine" is set to Grant and Login is enabled.
If that is set up that way and you're still having problems, verify that the protocol (either named pipes or TCPIP) is enabled for the server, if this is disabled it will prevent you from making connections from other computers.
edit
sounds like you don't have mixed mode authentication turned on.
In SSMS, right click on the server name and go to properties.
Go to the "Security" item on the left.
There are 2 radio buttons at the top:
Windows Authentication Mode
and
SQL Server and Windows Authentication mode.
You want to check the 2nd button.