Having dealt with A1181 button issues for many years now, I've found the situation often cannot be resolved, but the first and most effective step to take is to remove the battery (and make sure the battery isn't swollen -- that will cause a problem in itself) and firmly press up on either side of the button from inside the battery cavity. This will usually cause a cracking sound, as a seal formed by years of gunk buildup is broken. This alone will often restore the "click" to a "soft" button.
If that doesn't help, take a look at the underside of the button -- you'll see there is a strip of metal down the center of the button. Take a pair of tweezers and slip the flat end into the small space between the left side of the button and the metal strip, and then pry slightly, making the small space first about 1mm, and then if that doesn't do it try 2mm. This reduces resistance between the left side of the button and the "clicker mechanism" and often restores usability.
But if that doesn't help, it's most likely a lost cause. These topcases are flimsy, and the more you mess with them , the less the chance they are ever going to work again.
Also, as one final thing to try, put the battery back in and see if the push of the battery against the underside of the button helps -- sometimes it does. OEM batteries are best for this since they tend to be thicker.