Are you talking about the buttons on the laptop or in general even with external mouse? If it does not work on the laptop boot into safe mode and see if it works there. Make a Linux Live boot disk, boot off that and see if it works there. If not, contact ASUS support since it would be a hardware issue. Or replace the part if it's out of warranty.
Almost all laptop models can disable the touchpad after pressing a special key combination (it can be pressed accidentally). Some laptop models have an option in the settings of the touchpad drivers, according to which the latter is automatically disabled if a pointer (mouse) is connected to one of the USB ports or typing on the keyboard occurs. The pointer can be disabled in the BIOS like any other peripheral hardware. Sometimes the standard drivers may not fit the touchpad.
Find the key combination that turns off the touchpad. On most, these are the Fn buttons and the touchpad icon.
Make sure that a third-party mouse is not currently connected.
Open Device Manager and make sure all devices are healthy and functional.
If your computer came with a CD with drivers, you can try to install them from it.