Assuming this computer is out of warranty are you willing to start taking it to pieces ? Of course if it is still in warranty take it back to your supplier.
Without knowing the model of this laptop it is impossible to say how complex an operation replacing the trackpad would be - it can vary hugely. But as a first step download the manual, and the servicing manual if you can get it, from the ASUS web-site and then search YouTube for 'Asus make and model + replace trackpad'. This information will enable you to decide if you want to do this yourself.
If you don't feel like doing this then, as has already been suggested, disable the trackpad and use a mouse.