this is what i get as soon as i add an HDRI : https://i.imgur.com/VldQuMP.png
what did you do to make the light not come in from the deleted front face ?
thanks
Check this part of this video: https://cgcookie.com/lesson/reducing-noise-with-portals?wtime=44
In his 3D viewport you can see he extended the box out in order to capture his camera and then added a face to close the box. Once you do that the HDRI will only be able to light thru the window.