In short, you need a secondary login/authentication system. One that is NOT tied to the OS. Only the user can give out the login password. Period. You'd have to prompt for it. And to be honest, thats a very unnecessary security risk you would be implementing (saved passwords, sniffers, storage attacks, etc).
Its not clear the logic or reasoning for implementing this. If you want Windows authentication, you're going to have to do it with VPN. And at this level, the OS will take care of doing all the work.
I've done some work with Windows user names to automatically identify who was using an intranet application and what application permissions they had. But all we needed was the user name since you had to physically log into the machine to acquire the user name. We just put the user name in the database and tracked it from there. The users didn't have to log into the app and the app immediately knew who was using it. But in this case, the account's password was not needed.
Again, if we knew what the requirements were for this site, we may be able to provide you some alternatives.