shows apple logo when plugged into a power source but doesnt turn on

Okay so I don't know what may have triggered this as my phone has been working decently asides a broken home button, however, my phone died and I plug it in and it shows the apple logo screen however after around 30 seconds it returns to the black screen. I've tried plugging it into my computer however the same thing occurs and my laptop does not recognise the device either so I am unable to connect to itunes. Furthermore, my home button doesn't work so I can't do a hard reset...what do I do?! my phone is my life and I can't afford a new one atm