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.
In regard to slowness, you may want to clean up the computer. Uninstall unused programs. Clear all cache's and histories to browsers. Clean out temp files, run some good deep virus and malware scans. Also try checking to see what programs auto start when the system or Windows starts. If there are things (other than system items) that are starting automatically that don't need to, then I would change that.