MacBook Air - Won't Turn On (But it is charging!)

No damage, no dropping, no liquid etc.

The power cable is green, so I know it is charging.

Was working as per normal yesterday.

Today, tried to turn it on and it wouldn't turn on.

Did a reset, and it came on.

Was able to access the desktop for around 60 seconds.

Then it turned off again + won't turn back on.

I have tried doing the reset options (SMC + NVRAM), but no luck.

Can hear the fan turning itself on/off when I attempt to do the resets.

Older model, so out of Apple Care Warranty. But looked after, with no damage.

Local Apple Store has no appointments for a week.

Any suggestions?