NOTE: If you need to type in a password to even get into Windows to do the following, make sure you attached an external keyboard first, to get past the password. Then disconnect the external keyboard and try the following...
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.
Try the following and see if it fixes it...
1. Go into "Control Panel".
2. Click "Hardware and Sound".
3. Now click "Mouse and Touchpad".
4. Now go to "Additional mouse options".
5. The Mouse Properties window will open. In here click on your device.
6. Make sure your device is set to enabled. If it isn't then click "Enable Device".
7. Exit both that screen and "Control Panel".
If this does not help, and an external mouse works fine, then it may well be a hardware issue.