Connect to a website that has credential

You need to add an "Authorization" header to your web connector via the advanced tab when you enter the url in Power BI. The authorization header accepts the Basic encrypted credentials that are sent when you login to that site in your browser.

I used Fiddler to monitor the web traffic going in and out from my browser to see the Basic encrypted credentials that are used when I log into the website (under the raw tab in Fiddler it will say "Authorization: Basic (your encrypted credentials)". You could probably use some kind of encryptor website that takes your credentials and provides you with the Basic encrypted string, but I didn't think of that when I did this.

Edit: And this is how you can do it without Fiddler, go to https://www.base64encode.org/ and type in your credentials like so: 

                 "username password" 

With a : instead of a space no quotes obviously. Hit encode and now you have your Basic encrypted credentials. You can probably write this in M and replace the Authorization header code with a Base64 function in M but my M ain't exactly advanced.

Finally, under HTTP request header parameters in Power BI I chose "Authorization" as the header type and entered in "Basic (encrypted credentials from Fiddler)"

This worked for me.