My new Acer Aspire 7735G laptop keeps shutting down every 20-30 minutes and restating without any warning?

Time it to see if the intervals are exactly the same every time it shuts off. If they are, it could be that you have a non-genuine copy of windows and therefore need to reinstall the operating system (OS) with a genuine copy. When I ran windows 7, I didn't realize my trial had expired, so every 30 mins the computer would restart without warning. Besides it restarting every 30 mins on the dot, it worked fine.