To be honest, it sounds a lot like how one acts when something has been spilled on it, but try the following.
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/reconnecting 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.