DISCLAIMER : THIS PROCESS MAY DAMAGE THE PHONE AND RESULT IN A SHORT CIRCUIT IF NOT PROPERLY DONE. TRY IT ON YOUR OWN RISK
I fixed the water damaged home button on my S3 by sending a bit higher current through the home button flex contacts. You can easily find those two relatively big CONTACTS ON THE SCREEN SIDE when the motherboard is removed.
I used a 3V battery in series with a digital amp meter and a torch bulb(for current limiting) . Initially press the home button a bit hard and send a few pulses ( NOT LONGER THAN 1 SECOND AT A TIME )
If used for longer time it may permanently damage the flex cable or home swich , although there is no chance to affect anything else if done carefully.
DON'T USE THIS FIX ON MOTHERBOARD SIDE CONTACTS )