iPhone 4s screen problem

My old IPhone 4s has run into a strange issue. I have replaced the battery thinking that it was causing the black screen but it looks like tht is not the issue. If I disconnect the battery and leave it off for a minute or so the phone will come on as usual. When I power down it will not restart until I disconnect and then reconnnect. I only use the phone as a music player but would like to get it working again. It also appears that the home button has stopped too, I am not sure if this is linked? Odley when attempting to turn on it does appear to switch on but with a black screen. Any ideas