No signal on external monitor to macbook air 2012?

Question

Monitors

There are:
- macbook air 2012
- minidisplay port adapter - HDMI
- HDMI cable - HDMI
- Benq EW2420
monitor determined correctly. Exactly to the model. Tried other adapters and programs: SwitchResX. I also poked a wire from a working bundle of a monitor and a 2011 macbook pro to myself - the same result. Those. the problem is not the wires.
I wrote to apple support, but a month has already passed since the first appeal, and I only have a disappointing answer from the engineers:

Apple осведомлена о такой проблеме и выполняются работы по её решению. Вам предложили  следить за последними обновлениями которые будут выходить, так же если это возможно произвести подключение через адаптеры Mini DisplayPort->DVI или Mini DisplayPort->VGA.

Actually, it does not work through VGA either. The problem is most likely at the driver level.
Question: Is there a solution to this problem?

Answer 1

Working MiniDisplay Port (Thunderbolt)→HDMI-DVI Griffin

Answer 2

Aren't the new Airs Thunderbolt?
Sorry if I'm far from it, I just don't know about compatibility myself.

Answer 3

Result:
DisplayPort->DVI refused to work the same way on the MacBook Pro 2008, which I used to always connect like this (?)
Solution:
DisplayPort->DVI-> DVI / HDMI->HDMI TV
Both Air and Proshka worked in this bundle.

Answer 4

I'm fine with the same beech:
MDP->adapter->VGA