would it be possible for you to get into the windows log, see if there is any obvious errors in there.?
or can you boot into safemode? can you hook it up to an external monitor, see if it gets the same pixel errors?
Try taking out the battery and the powercord. keep the power button down for 10 or so sec, then leave it alone for 5 min, hook up the battery and try to boot only from battery.
It could be a dying harddrive.
error in the GPU.
Since you got it some weeks ago, I would say get it replaced at the spot you bought it from.