I've seen several post where people have a home button that stops working. Upon closer inspection they find that one or both of the contacts are missing from the ribbon cable that is attached to the home button. This also happened to me, most of the fixes I've seen involve separating the digitizer to replace the home button assembly. I didn't want to do that so I came up with another method. You don't have take apart your digitizer and you can fix it in just a few min. It is a bit tricky however so make sure you have a good understanding of what is going on before you proceed! You will need a some piece of old electronics like a circa 1980 calculator or something that had a LCD display on it. Why? Well old LCD displays used a kind of silicone rubber strip that have carbon "wires" printed in it to carry the signal from the PCB to the display, a piece of this strip is what you can use to replace the broken contacts of your home button.
WARNING: this requires taking apart your iPhone and will void your warranty, You should be patient and have steady hands to work on an iPhone or you could break it more that it already is!
1. Remove the front LCD/digitizer assembly from your iPhone, There are plenty of descriptions on how to take apart the iPhone so I'll skip that part.
2. inspect the contacts of your home buttons ribbon cable located on the back side of the LCD/Digitizer under the home button:
You can see what the contacts should look like in the photo below, they are the two gold colored metal pieces on the lower right side of the photo.
if they look intact, as in this photo, STOP there is something else wrong and this will not help you.
3. If one of the contacts is broken, this will work for you but you will need to remove the other one as well. Using a small flat blade screwdriver slide it under the free end of remaining contact and pry up. this should not take much to break it off.
4. Check that the broken pieces of the contact are not in your iPhone, you may want to use some computer dusting air to lightly blow out your iPhone
5. Take apart the old LCD display, The image below shows a display taken apart to expose the rubber contact strip (the long price on the PCB, it is not attached to the PCB only sitting on it and can be just lifted off) you won't need anything else from this display and it can be discarded.
Note that black stripe down the center of the rubber strip? It is the conductor strip and will need to be properly oriented for this to work.
Basally this strip is two prices of rubber that are sandwiching a bunch of tiny carbon wires sitting on end so that the signal can be carried from the contacts on PCB to the display contacts directly above. Make note on what side is facing the PCB when you remove it.
6. Carefully cut a 5mm section of the end of the silicone strip using a sharp razor knife. Make sure not to use much pressure while cutting or you will misshape it. also keep track of what end was facing the original PCB.
7. Trim the height to 2mm-3mm if needed to allow it to fit into the iPhone (note that you may have to adjust this a bit, be careful and don't force anything)
8. Reassemble your iPhone to the point of pushing together the LCD /digitizer assembly back into the case but don't push it in yet. Hold you iPhone so that you sill have a 4 cm gap and the digitizer (front of the iPhone) is facing down.
9. place the trimmed piece of contact strip on over the area on the home button ribbon cable that used to have the contacts, Make sure to face the side of the silicone contact strip that you noted as facing the PCB in step 5&6 toward the contact area on the lcd/digitizer assembly.
10. Carefully close up your iPhone and replace the screws.
Good Luck!
WARNING: this requires taking apart your iPhone and will void your warranty, You should be patient and have steady hands to work on an iPhone or you could break it more that it already is!
1. Remove the front LCD/digitizer assembly from your iPhone, There are plenty of descriptions on how to take apart the iPhone so I'll skip that part.
2. inspect the contacts of your home buttons ribbon cable located on the back side of the LCD/Digitizer under the home button:
You can see what the contacts should look like in the photo below, they are the two gold colored metal pieces on the lower right side of the photo.

if they look intact, as in this photo, STOP there is something else wrong and this will not help you.
3. If one of the contacts is broken, this will work for you but you will need to remove the other one as well. Using a small flat blade screwdriver slide it under the free end of remaining contact and pry up. this should not take much to break it off.
4. Check that the broken pieces of the contact are not in your iPhone, you may want to use some computer dusting air to lightly blow out your iPhone
5. Take apart the old LCD display, The image below shows a display taken apart to expose the rubber contact strip (the long price on the PCB, it is not attached to the PCB only sitting on it and can be just lifted off) you won't need anything else from this display and it can be discarded.

Note that black stripe down the center of the rubber strip? It is the conductor strip and will need to be properly oriented for this to work.
Basally this strip is two prices of rubber that are sandwiching a bunch of tiny carbon wires sitting on end so that the signal can be carried from the contacts on PCB to the display contacts directly above. Make note on what side is facing the PCB when you remove it.
6. Carefully cut a 5mm section of the end of the silicone strip using a sharp razor knife. Make sure not to use much pressure while cutting or you will misshape it. also keep track of what end was facing the original PCB.
7. Trim the height to 2mm-3mm if needed to allow it to fit into the iPhone (note that you may have to adjust this a bit, be careful and don't force anything)
8. Reassemble your iPhone to the point of pushing together the LCD /digitizer assembly back into the case but don't push it in yet. Hold you iPhone so that you sill have a 4 cm gap and the digitizer (front of the iPhone) is facing down.
9. place the trimmed piece of contact strip on over the area on the home button ribbon cable that used to have the contacts, Make sure to face the side of the silicone contact strip that you noted as facing the PCB in step 5&6 toward the contact area on the lcd/digitizer assembly.
10. Carefully close up your iPhone and replace the screws.
Good Luck!