My eMachine E627 has a separate button (to the left of the main power button) which disables the touchpad. If the orange indicator light is on, the touchpad is disabled.
My search for what was wrong (I didn't know about the button, nor that I had pressed it, and the setting is remembered even after reboot!) was complicated because the Touchpad does not appear under 'Human Interface Devices' in Control Panel, as other mice do. It is under 'Mice and other pointing devices' though - I didn't notice that group!