Chosen Solution
I have a macbook air that on boot up stalls at the grey apple screen and the loading circle freezes and it stops booting and sits there.
Do you have a second Mac system? If you do connect your Air to it via Target Disk Mode to gain access to the Air’s drive so you can run Disk Utility on it. Reference: How to use target disk mode to move files to another computer
A friend of mine had a similar problem to this on his macbook air This may not be the case here, and i don’t want to jump to conclusions, but in the end for him, it was a build up of bad sectors on his SSD, and he had to replace it (ebay) In this case, it may be something much simpler, take the advice from dan, OR Have you tried to boot into safe mode? - Hold down Shift (⇧) after pressing power, and continue to hold until you boot into safemode OR - Read these other simple tricks - like holding down ’ D ‘ for apple diagnostics https://support.apple.com/en-us/HT201255
