I have SQL Server 2010 running in windows auth mode and the proper groups have been assigned. I can connect via the SQL Server Client Studio using windows auth. That works. But
According to http://connectionstrings.com/sql-server-2008 this should do the trick
Provider=SQLNCLI10;Server=172.20.0.113;Database=ForgeEnterprise;Trusted_Connection=yes;
Where Trusted_Connection is the same as Integrated Security apparently.
If that doesn't work, you should verify that the user is added in the permissions tab (picture) for the database, but I guess you already did that.