Sorry, I didn't read closely enough, I see you are using a windows web server. I thought you were using a *nix server.
From a windows IIS server, if you want to use windows authentication the web server will be operating in the IUSR_computername user account unless your web is authenticated. If users must authenticat to windows, then the web server will impersonate the logged-in user.
The IUSR_computername user account is a local account to the web server normally, so if the SQL server is on a different box you will need to create a clone user account on the db server. In addition, any authenticated users must have a corresponding user account on the db server.
Then you must allow the proper db access to these windows user accounts and at that time you should be able to connect using windows authentication. Don't specify a user or password in your connection string.
hth