Does your computer have the acu-pointer, the eraser head looking thing in between your keys or a nice flat touch pad??
It could be a bad keypad (keyboard) ... Intermittent connection that acts up when typing keys and the pointer rehomes at the center of the screen by your system when it reestablishes connection with the pointing device. :-/
Try leaving your pointer pointed in a corner on empty desktop and start typing like you are typing a report. Does the pointer still go back to center position??? If so, you have an intermittent connection probably...Maybe its just a loose cable inside, otherwise a new keypad could be needed...
Has this laptop taken any abuse, knocks, falls, anything spilled on its keys??? :-?
*** Also... Your laptop could use more Ram, 128MB is bare minimum for XP Home, when it is probably sharing memory with the video GPU. This memory size would not cause the issue though...