I usually don’t suggest “wipe the hard drive” so soon, but if this is really such a new Mac you probably don’t have much personal data on it, right? I suggest getting your files off of it and starting fresh.
Put the OS X disc that came with the computer in the disc drive and re-start holding the “C” key. Once it boots, find Disc Utility and erase the Hard drive with the Mac Extended format (Journaled).
Then use the CD to re-install OS X and go from there.
If this was a computer you’ve been using for months it might be worth tracking down the problem, but since it’s so new it may be impossible to figure out the one single thing that’s wrong. Most trouble-shooting involves examining recent changes to the system…you can’t do that since you haven’t had it long enough to have a history with it.
I’d just start fresh and see if that works. If it doesn’t then I’d say a hardware problem is likely and you should contact the store you bought it from and get a replacement.