"Added an IIS User" -> Do you mean IIS Manager user?
If so, these aren't real Windows users - just a username and a password in a text file somewhere: they don't have a SID or security tokens, and can't be used for Basic authentication. Not using the out-of-the-box configuration, anyway.
Create a (real) Windows user, and it'll be usable for Basic auth.
Edit: I just noticed you said something else - Feature Delegation doesn't describe permissions to the site contents, it's whether a non-Administrator can configure those features at a lower level within the site in a web.config file - essentially, which IIS feature icons are usable when they connect to the computer via the Management Service.
The answer is roughly the same, though:
- reset delegation to defaults (you didn't mean to change it; it's dangerous to change some of the delegation settings from defaults under these conditions)
- create a Windows user in Server Manager
- assign permissions to that Windows user either at the file system level, or using the URL Authorization feature