Will a Touchpad Replacement Fix My Floating Cursor?

It could be the touchpad, but there's a chance it could also be the little red "Trackpoint" in the center of the keyboard. The way the mouse is drifting instead of bouncing around defnitely seems more like a trackpoint problem. To confirm this, I'd disable the trackpoint in Device Manager. To do this, type Device Manager into the Start Menu. When it's open, go to the pointing devices section (I think). In that subcategory, you should find your trackpad and trackpoint. From there, double-click the trackpoint, then click disable device in the window that comes up. If the problem goes away, you know the trackpoint is at fault. If it isn't something you use much, you can keep it disabled. If the problem persists, you should start looking into a trackpad replacement.

If you have any more questions, just leave a comment.

Hope this helps!