Buy a new one or fix this one

1. First thing you could do is to apply some new thermal paste to the CPU in the ASUS. If the CPU overheats it will shut down to protect itself.

2. Replacing the motherboard on any laptop is a very complicated and time-consuming operation. Between the time spent and the money expended on a new board, you're almost better off buying a new laptop. And that's going to be my advice.

3. If the Acer A715 you're considering is this one:
https/www.acer.com/ac/en/GB/content/model/NX.GP8EK.004

...then it's certainly a very attractive machine with great specs. My only reservation is that Acers are generally high on specs but low on build-quality. This means you have to treat them very delicately. The ASUS FX553 is a stylish rival with almost identical specs, like this one:
https/www.asus.com/Laptops/ASUS-FX553VD/

Between these 2 I'd go for the ASUS.

4. As a regular person you can perform a clean format of your hard disk. This will prevent other regular people from accessing your old files. If for various reasons you're particularly worried about 'special types' of people being able to access your disk, then you need either specialist software (the kind used by law enforcement) or to send the disk to a specialist business that can wipe the disk completely.

Cheers,
GreyCatz.