Hi,
Check out this article to troubleshoot this issue;
https://support.apple.com/en-gb/TS2570
My friends macbook air was working fine. It began to slow down on startup and reset the date and time. It was really slow opening finder windows especially, and just generally clicking on anything brought on the spinning wheel. After a little while it just wouldn't start up and went to a blue screen. After a little while longer it would only chime then go to the grey apply logo with spinning wheel underneath.
I've tried resetting pram and the other thing, and tried safe boot. The details I get with safe boot end in 'waiting for dsmos' (i think). I have no disc drive for the install discs. I have what is meant to be a bootable USB but the Mac doesn't recognise it when I try the other boot options. I have an external hard drive, if I put a .DMG of snow leapord (which I believe the macbook air to be running) on the HDD would this help me? I qm only semi Mac savvy but willing to try anything with a bit of instruction so any help is most welcome. Any more information needed I will find if I can! Thanks in advance!

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