A1466 covers 5 years -- 2012 to 2017 models.
I have a 2017 MBAir that simply stopped doing anything.
I set it aside, didn't touch it for several months. So, the battery had died completely. Again, several months later, I took it out of the box, with several other "dead" laptops, just to see if there was anything that I might be able to use.
I plugged that MBAir to the charger, and left it for about 30 minutes, then tried to turn it on...it worked! Now, about a year on, it is my main "slightly older" work laptop. I put in a new battery, and now have an NVMe boot drive, which is significantly faster than the original Apple flash storage.
It's a nice, very usable laptop.
Is your screen completely black? Or just no backlight? Turn it on, leave it on long enough so something should appear on the screen, then shine a bright flashlight into the screen from various angles. You would be looking for any graphics on the screen, like a menubar, or icons/dock - or just a login screen. If there is video, you should see something, even very dim with no backlight.
This is what I would do: bottom cover off, disconnect the battery, and just leave it that way for a couple of days - don't touch it in any way. Is there any kind of visible swelling on the battery? If you see anything that you think is swelling (it should be obvious to you), then just replace the battery. It's quite easy to replace, go to iFixit.com for some help if you need it for removing that battery. If no problem with the battery, after a couple days, re-connect, put the bottom cover on, plug in the charger, don't touch anything for 10 minutes or so.
And, press the power button. immediately, first reset SMC by holding Shift-Option-Command, then press and release the power button. Do the same reset a second time. Then, do the NVRAM reset (press and release power button, then immediately press and hold Option-Command-P-R. You should hear a boot chime. KEEP HOLDING the same 4 keys until you hear the boot chime 2 more times, then release the keys, except for Option. You should get the boot selector screen, so wait for your boot drive to appear, then click on that, and press enter to boot up.
( You will notice that neither of those resets require you to see anything on the screen
)
Assuming it boots successfully, open your System Preferences, then Startup Disk pane. Click on your boot drive, so it is selected. (the NVRAM reset clears that startup disk preference, so it is good practice to make sure it is properly set.)
Did any of those steps fail to work for you?