Acer Aspire v3-771g random shutdowns

I bought the Acer Aspire v3-771G. I've had no problems with it, but lately it shuts down randomly without any warning, like a power cut. I've checked the CPU Temps and overheating is not the problem. The computer sits on a Targus cooling pad and it dosen't get that hot around the fans. The problem occur when the pc is running games or processes (computer scans) that require more memory than when I'm just surfing. The problem happens all from 15 mins to 2 hours into a game or so (depends on how much memory that's used). I've been doing some research myself and it seems like a graphic problem.

The computer always fits the minimum requierments for games I play and I play on rather low graphics on every game (to delay the shutdown).

The second problem is whenever I'm streaming or wathcing a movie the screen randomly turns into a "snow storm". Tried to move the screen up and down thinking it was something wrong with the cable from the hardware to screen but it didn't react to that. I have no idea what has made this to happen due to the careful handling of the computer. But the only thing that comes to mind is something wrong with that cable... This problem happens randomly and started last week.

I've done some basic problemsolving, with no succes. I've tried restoring the computer to facotry setup, updating the bios and all the relevant drivers. 

I've been looking for a hardware diagnostic program on the computer itself (like other good brands have) with no luck, even looked on the web. But nothing I've tried seems to find the problem. 

The specs for the computer:

Acer Aspire v3-771G

Windows 8.1 (Came with Windows 8.0)

Intel(R) Core(TM) i3-3110M CPU @ 2.40GHz  2.40

8.00 GB (RAM)

64-bit operating system

Nvidia GeForce GT 630M

It's a clean computer carefully handled and sits in low dust enviorments (not in the bed) with no scratches or bumps.

Any tips or whatever is thankfully taken.

Any ideas before I have to send it to service?