If it is hard, stiff, apply more strength before you get a click. It is most likely due to swollen battery. FYI there are only one physical click button at where you marked green. Clicking too far at the edge might not register the click. If it is not due to swollen battery, a service and adjustment to the trackpad mechanism will usually solve the issue.

I will not wait if there is a swollen battery inside the unit.

There are no more original battery and most part for this model as this model is already vintage and obsolete. Many seller/ repair shop would simply say their parts as original new, which they hope you never find out.