A few more details about the story of your machine might be helpful. For instance, is it a new Laptop? If not, did it use to work well before you installed 12.04?
So I just assume the Laptop is new. Based on my very personal experience, it might be that you are experiencing a RAM failure. I bought a Laptop and I installed Ubuntu (11.04 at that time) on it. I started experiencing some random freezes, like those you described (mouse cursor not moving, keyboard not responding). I turned out that it was an hardware problem and I had to give that Laptop back. Running a memtest might shed some light on your case.