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.
Now should that not help, and the external one you stated works fine, then it could be the keys themselves that are the issue. Meaning you may need to replace the keyboard.