If the cables are all fine, or making sure the cables are firmly placed does not work, check the dock connector for any broken pins, especially the areas I highlighted with the circular red markers. If any pins are broken, you might want to buy new cables, because repairing these pins requires a lot of experience and precision tools.

If this STILL doesn't work, check the pins on the cables connected to the home-button (marked with a red marker in second image.) Again, if any pins are broken, you might want to buy new cables, or a new home-button, because these pins are very fragile and hard to fix.