I've had the problem on a couple of laptops, and it was - in my case - caused by dragging a thumb on the touchpad while typing. The touchpad can be disabled in Control Panel, or with one of my old laptops with a "mouse program" that came installed.
With the touchpad disabled though, you likely will want another pointing device, unless you're the sort of "really casual" kind of person who likes watching the cursor slowly twitch across the screen while you use the wobble-stick that's also on most laptops.
With both of the laptops where I had the problem, the touch pad used the same port as the "serial mouse port" so that plugging in an external serial mouse (standard mouse or track ball, turns the touch pad back on, so the keyboard problem returns. These both were old models, and you may not have that problem with a new one, but if you have an old serial mouse you might want to try it before buying a nice shiny new one for the laptop.
The solution I used was a USB mouse. Since the USB port is separate from the serial port, it can be connected while the touchpad remains turned off.
If the way you plan to use your laptop isn't compatible with using an external pointing device, you're only real solution may be to learn to type with your thumbs pointing up and hands off the surface of the machine, or do a detailed study of "how to run your computer without a mouse."