Having real issues

About half a month ago my Ipod touch 5th gen's home button started to fail. which resulted in it having t be pressed a lot harder then it need to be . Today the Ipod has just stopped working altogether . I have tried to book it if for a service but because I have find my ipod turned on it will not expect the serial number I have tried to follow the on screen instructions to turn it off but still it still wont expect the serial number. I would really like to get it fixed as soon as possible but I seem to be getting stuck even before I start can anyone help me out with this?