MacBook Air 2013 bad wifi when internal monitor off while using external monitor

As absurd as it soundsmy macbook shows the connection to WiFi but does not load anything when connected to external monitor.

I use MacBook Air 13 inch 2013 1.7 i7 chip and 8gb ram and DNS L270 1440×2560 monitor connected via display port and mini dp to dp adapter at 60 hertz (NTSC)

Here is how I came up with my conclusion:
The way I use them is by having both on the desk, I mirror displays so I only use the external monitor a mouse and a keyboard, while my macbook is open and left aside with the screen brightness turned to none. I was bothered with poor wifi on the MacBook for some time, while other devices worked just fine in the same room. Sometimes I would take my MacBook and go to another room to see if wifi works better on it and it did. This morning I got pretty annoyed how I could not open a news article in my room, but could stream 1440p videos on Youtube no problems just outside the room. So I grabbed my desk out of the room and to my surprise it still would not work properly. However as soon as I unplugged the external monitor, the wifi works just fine. After a few 'try and see' I worked out that wifi works fine when the brightness on the internal screen is on. I have no idea why it works like this and I am probably wrong with my guessing.

My problem is to have wifi work while the internal monitor remain none of the brightness.

When researching on this topic I found this and looked into it. However I never shut the lid so it's not a case here. Apart of that question I could not find anything close to my problem. So I wonder if anyone had a similar issue and any possible solutions?