When you uninstalled the driver, did you make sure to reboot (power totally off and then back on) the laptop and letting the computer install the driver itself? If you didn't do it that way, then the driver likely didn't get changed. So I would try that.
If that doesn't resolve it, then you may well have something on the laptop. Virus, malware, bad program, etc. Try launching the computer in "Safe Mode" and see if it happens in there. If it does, then it is likely hardware and you may want to either have the keyboard replaced or have the laptop looked at for other problems.
However, if the problem doesn't happen in "Safe Mode" then you need to do good deep scans on the computer for viruses, malware, etc. and remove whatever is the...