I'm an Apple tech.
NO SUCH THING AS FLAT RATE LIQUID DAMAGE REPAIR. Its called you just voided your warranty,
A flat rate repair is retail cost for your laptop....lol
If you take it to an apple store and show it to them EVEN after you try there are liquid sensors inside the laptop that only a tech can get to. If they see any liquid sensor tripped you have just 100% void your entire apple care or one your limited warranty.
DO NOT PUT IT IN RICE. As much you as see idiots doing this you are already TOO FAR GONE to try and get any sugar from the coffee off your logic board.
You obviously blown multiple capacitors that control the voltage to the backlight.
With a MBA there really isn't anything you can do besides buy a new one.
A new logic board, which is what you will need, parts and labor is about $450-800.00 depending on the model/ ram configuration.
Then you will need a new top case , parts and labor your looking at $150-300.00 depending on size and age of the MBA.
New SSD (With MBA liquid spill apple will require you replace the SSD blade drive because it is technically part of the Logic board, but you would be charges separately. They will not warranty a new Logic board with an old SSD with a known liquid spill.
And if it is an early MBA with a HHD with a ZIFF adapter, it should be fine if you can boot the machine with no issue.
Last, a new battery, once again Apple will not warranty a new battery if the system has been victim on a liquid spill.
This is not true for most models, but always in a Macbook Air.
You might as well sell that on ebay , and let some self proclaimed wizard let him self think he can fix it, so just sell it.
Then buy a new one. Thats pretty much all you can do.