Well it could be the keyboard itself, it could be the driver or it could be a virus or malware.
Start with this...
1. Uninstall the keyboard driver.
2. Reboot the computer (without reinstalling the driver).
3. When it restarts, it should reinstall the driver on its own.
If this doesn't work, you may wish to try connecting an external keyboard and see if it works fine. If it does, then it could be the keys themselves that are the issue.
You may also want to try updating the Synaptics Driver if the above doesn't help.
Now if that stuff doesn't fix it, then I would try starting up the computer in "Safe Mode". If it loads and doesn't do that in "Safe Mode" then you have something fishy on the device. NOTE: Not all things run in "Safe...