If you happen to have an external display, adapter, and cable that fits your MacBook Air display port
this may be a way to test the graphic section of the logic board. Because I've no MB/Air model to test
how this may work, I cannot say the process to ensure the external display could help. ~ An early 2015
MacBook Air could use Thunderbolt2 and minidisplayport to connect to external; later 2015+ would
have the newer USB-C port.
If you have an external keyboard and mouse, (wired) the MacBook Air may be turned on in Clamshell
Mode and an external display forced to be used as Main Display; if the graphic chip on logic board is OK.
These options may exist if you have and know how to use them; an authorized independent Apple service
could troubleshoot your Mac with sufficient skill and additional hardware.
Later MacBook Air (after 2015 Retina) have no traditional display port; from what's been said, they went
to USB-C ports and require correct cable to connect external displays. To determine a course of action in
the path of Troubleshooting the Graphics, you'd need to check the Port to see if its a newer USB-C ~ then
if you have a display to test this with, pair them via an adapter or other accessory.
Not sure if there's some kind of screen sharing that could work if the MacBook Air has defect in hardware.
Sadly if there's no independent authorized Apple service/sales business in your location, you may not be
able to get the unit to respond. A service technician could try & troubleshoot; then perhaps initiate a repair.
A 'VGA USB-C multiport adapter' (apple) may be the correct one needed; how to go about starting MB/Air
to see if that'd help, is another matter. ~ Could be a keyboard shortcut; I don't know. My old MacBook1.1 is
the first build 13- inch model from 2006, and uses regular ports.
There may be a few helpful links (to hardware repair, third-party 'independent' authorized Apple service?) from:
• Genius Bar Reservation and Apple Support Options - Apple
https://www.apple.com/retail/geniusbar/
If your product was registered with Apple under your Apple ID the above site may (or not) be helpful.
The page is divided into two sections, Software and Hardware. When I use it (logged in here) I see my
own stuff and near where I am, ~ and cannot search for Locations elsewhere.
There may (or not?) be an independent Apple authorized service provider in the region you are now.
Use the blue word/link to open page to find selection of nearby locations for Apple-certified repairs.
That blue link should actually be: https://locate.apple.com/