iPhone 5 not working suddenly. Stuck at apple logo. Not entering DFU Mode also. Not recognised in iTunes also. Running 8.3. Not jailbroken. On pressing home and lock screen stuck at Apple logo and then after some time screen goes blank.

I am using the iPhone 5 for 2 and a half years and it was working fine, when suddenly one day the phone got hanged and went to the Apple logo and it got stuck there. I tried to hard reset it but to no avail. I even tried to enter DFU mode but it is not doing so. I tried all the possible tricks to go tot he DFU mode but it is not responding and not doing and is stuck to Apple logo and then after some time screen turns blank. Also when I connect the iPhone 5 to Mac or PC, it is not recognising in iTunes. I also checked my iTunes is up to date. My iPhone is running on iOS 8.3. I also submitted the phone to Apple Service Centre. They robbed me of Rs. 1,400/- ($30 USD), kept it for 1 day and then rang me up and told I have to spend Rs. 21,000/- ($400 USD) more and they will get me a new phone. I did not went for this offer and also checked back that they even did not open my iPhone to test it as I have a glass screen protector and if they have opened it for testing the glass protector would be peeled off atleast. So please help me what to do.