It sounds like the very bottom of the list might be hidden by the Windows taskbar at the bottom of the screen. So try this:
Right-click on the Windows taskbar (the taskbar is the strip from the Start button to the clock, click on an empty part of it).
Click on 'Properties'.
Tick 'Auto-hide the taskbar' and click 'OK'.
You should now be able to see the bottom of the Google search list, where it says 'Clear History' in blue on the right-hand side.
You can go back to taskbar properties to change the setting to how it was before.