It could still be the trackpad driver (or even something like a buildup of static electricity, etc). Many laptops from different manufacturers use similar trackpads manufactured by Synaptics and there is often an updated driver and utility to manage the settings for sensitivity and “palm check” etc, that can be helpful. There is also sometimes an updated driver available from the computer manufacturer or through Windows Update. Updating that and also playing with the settings may help.
If it only started doing it after working fine initially then you could also try a hardware reset, by shutting down Windows and powering off the laptop, then unplugging the AC adapter, and finally, taking out the battery. Then hold down the power button for several seconds and release it (it will look like nothing happened, but it does clear up some types of problems).
Then put the battery back in, connect the AC adapter, and start the computer back up to see if the problem might have changed or gone away.
In addition, some laptops have a small button near the trackpad that disables it. That comes in handy when doing a lot of typing, or if using a wireless mouse rather than the trackpad anyway.