Okay, so I have submitted this super simple HTML page here:

http://medicaldevicesgroup.net/wp-content/themes/medicaldevicesgroup/test.html

It's utilizing LinkedIn's "RegisterInch API. See the source. It's two lines of code. Nothing.

BUT

I produced a house.perl file during my child theme directory, and copied and pasted this:

<?php require(CHILD_DIR.'/test.html'); ?>

Which means that should you see the source at http://www.medicaldevicesgroup.net/, it's Exactly like the origin at http://medicaldevicesgroup.net/wp-content/themes/medicaldevicesgroup/test.html. The only real difference would be that the webpage is within WordPress, and also the other URL is not.

The house page script, however, does not work. WHY???? Help! Thanks.

This is because since the LinkedIn API that you're using is perfect for http://medicaldevicesgroup.net and never http://www.medicaldevicesgroup.net. Spot the "www" in second URL. You have to improve your URL within the LinkedIn API.

To determine what i'm saying try likely to http://www.medicaldevicesgroup.net/wp-content/themes/medicaldevicesgroup/test.html and it'll not work there too.