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You may have a hardware problem, but it's extremely unlikely it's a software problem or a malware problem
If it's a corded mouse or wireless mouse, some models are sensitive to even a tiny amount of vibration and the cursor will move when your hand is not on the mouse - place your hand on the mouse and hold it still - if the mouse cursor does not move, there's nothing wrong with the mouse.
If it's a corded mouse, it's common for wires to get broken inside the cord and that can cause strange symptoms - try a different mouse.
If it's a touchpad built into a laptop or netbook, you probably have a hardware problem - try a corded or wireless mouse.
You can RIGHT click on and Disable the touchpad in Device Manager.
If the laptop or netbook
- has been dropped, or has had something dropped on it, or has experienced a physical jolt
- has had liquid spilled on it, or has been exposed to liquid such as rain, or has been sprayed with liquid
that's likely to cause damage to the laptop that may result in the touchpad not working properly, forever.
If you have just cleaned off the touchpad with isopropyl (rubbing) alcohol, or some cleaning solution with that in it, I know from experience that the isopropyl alcohol is often absorbed into the touchpad such that even when it appears to be perfectly dry the touchpad will not work properly for quite a while - you may have to wait as long as, say, 8 hours, for the alcohol to completely evaporate from within the touchpad.
If it's a wireless mouse, they will not stand up to being dropped a lot, and they will malfunction eventually and have to be replaced - there is no fix other than that..