Open the onscreen keyboard and hit the H key and see if it actually activates another key. If it does then your keyboard needs replacing.
To enable onscreen keyboard in case you don't see it:
Open System Preferences and go to “Keyboard”, and look under the “Keyboard” tab
Check the box next to “Show Keyboard & Character Viewers in menu bar”
Pull down the newly visible Keyboard menu and choose “Show Keyboard Viewer”