I am pretty sure I know what your issue is, so bare with me here.
First, when you are typing, do you have your touch pad enabled? Do you have a mouse that you use with the machine? Do you use your built-in keyboard or an external one?
I have seen this a LOT, that when touch-pads get old, they get VERY sensitive to heat. What I am implying is that even if you are not bumping your touch-pad, it is sensing your hand heat from above the pad, and moving the cursor. As the protective covering wares off of the pad itself, this becomes quite common. To test this theory, turn off you touch-pad in control panel, and try typing a letter.
This (driver?) has been "driving" me crazy also. I'm running Windows 7 on a Dell Latitude E6500 laptop, and I only use the touchpad. I don't use the keyboard "pointing stick", and I've never even had a mouse attached to this. I made two different changes before attempting to check my results, so I really don't know which one fixed the problem. I guess I'm not much good as a scientist. I should have checked results following each change. Anyway, the problem is gone. (1) I downloaded and reinstalled the currently available keyboard driver, and (2) I went into "control panel", "mouse", and I disabled the "pointing stick". Now the cursor stays with me regardless of typing speed. I typed a test document in Word, I typed a long email note, and now typing this I have no problems.
very common problem with dell laptops. the touchpad goes flaky and begins randomly moving your pointer. normally the pointer goes to the same corner over and over but i have also seen some random movements. disabling the touchpad and using a mouse is the easiest solution.
getting dell to replace the touchpad is the only true way that i have ever seen to fix this issue. it's just a poor design on dell's part. try deleting and reloading the drivers for it but in the end you will probably wind up just using a mouse instead.
the government bought a ton of dell laptops and i can't tell you how many of them i saw with this problem. was between 50-60% that within a year wound up with this problem so it is a problem dell should have fixed by now but seems to not care about.
same proble, I also though it was a driver issue. I read somewhere it could be an issue of static electricity getting stuck in the touchpad... (inspiron 3520). It would make sens it's for me random, it comes and it goes...