MacBook startup sound loop
Since you've already reset both the NVRAM and SMC and established the SSD is capable of booting another MacBook, I'd try testing your MacBook Air hardware.

Run Apple Hardware Test

Your model of MacBook Air uses Apple Hardware Test. To use this, follow these steps:


Shut down your MacBook Air 
Restart your MacBook Air
Press and hold the D key before the gray startup screen appears.
After a while, Apple Hardware Test (AHT) will start.
When prompted, select your language and click the right arrow. 
When the AHT console appears, you can choose to run Basic tests by clicking the Test button. However, I suggest you select the "Perform extended testing" checkbox before you click the Test button.
Your test results will appear in the window in the bottom-right of the console.


Note 1: that the extended test will take some time. Take a note of the results and report back. 

Note 2: If pressing and holding the D key at Step 3 doesn't work, start again at Step 1 and, at Step 3 press and hold both the OptionD keys instead. This will try and run diagnostics from the internet instead, so you will need to allow more time for it to complete.

Once complete, let us know your results.