New laptop shuts down without warning

I have a gateway pc, had it is 5 months and for the last few weeks I will be on-line and it will just cut itself off. i will restart it and ask if I want to check for errors or start normal, sometimes it will start the first time and sometimes it will just keep cutting off and than after about 5 or 6 trys and start and run fine.
 
Does this only happen when online? If not, when else does this issue occur?

Do you get Blue Screens?
 
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