Windows 10: How do I fix this in my laptop?

I was playing video games when suddenly I moved my cursor down and it started lagging very bad. But when I put my cursor up it doesn't lag and operated normal I restarted the laptop when suddenly a gray screen appeared after a few seconds it changes to a white screen covering half of my laptop screen I don't know how this happends please help me.

:)

 

Best laptop under $800??

Well the last one I suggested seems to be the best for 650$

EDIT: to facilitate your search...

Laptop GFX benchmark list

Laptop CPU Benchmark list

 

Programs not working

In post 26 there were steps listed to fix the operating system corruption.
Are you able to follow them?
In post 29 was the suggested dism repair command.

 

I'm online from my wifi laptop but can't connect to my home network

Nope, I've tried all the steps of all the fixes listed by Dalchina and Try3 but the problem still exists. The W10 laptop refuses to access my main W7 pc (named CG16) on my home network, although it can 'see' it, ie, it shows CG16 in the network list. The only thing I haven't tried is Dalchina's suggestion about creating a shortcut, mainly because I'm not sure where this shortcut is supposed to be. I'm assuming it has to be on the W10 laptop but I don't understand how it could work. More info please, Dalchina, if you'd be so kind. Daymin, sorry: I have no idea what you're trying to say.