Hi and welcome to TSG.
Before a backlight / inverter totally fails it can run intermittently, so I wouldn't totally discount that option. Infact, based on your description I would consider this the most likely cause of the problem, it is also a common failing component.
When the laptop is on and the screen is blank get a bright torch and shine it at the screen, look closely at it and see if you can still see a feint image of the desktop and other expected information. If you can then the backlight / inverter need replacing.
Personally, I wouldn't expect the screen to go blank due to a fan problem, if it was overheating (likely if the fan was failing) it would likely alarm and shutdown automatically. I assume that the machine appears to be running still when the screen blanks out?
Before a backlight / inverter totally fails it can run intermittently, so I wouldn't totally discount that option. Infact, based on your description I would consider this the most likely cause of the problem, it is also a common failing component.
When the laptop is on and the screen is blank get a bright torch and shine it at the screen, look closely at it and see if you can still see a feint image of the desktop and other expected information. If you can then the backlight / inverter need replacing.
Personally, I wouldn't expect the screen to go blank due to a fan problem, if it was overheating (likely if the fan was failing) it would likely alarm and shutdown automatically. I assume that the machine appears to be running still when the screen blanks out?