In this situation Apple can actually be helpful, which is uncharacteristic. Usually a blockage or physical problem can be repaired and often it is a factory defect. Remember, if you are using a protective case this may be to blame for unresponsive iPhone Home buttons. If the solution is not dealt with by purely opening up the iPhone and cleaning it you may have to actually send it back, but if there are signs of physical trauma to the iPhone itself it will likely cancel out any protection over the device through the warranty. This is going to be especially true if there was any water damage.