Iphone 5 Not Charging - Please Help

So,

My Iphone had about 80% charge whilst playing music, the phone switched off, and had immediatly would not turn back on due to empty battery.

Charged the phone by mains power for 3 days, no joy. (tried for 2 hours with a brand new cable too)

Charged the phone by USB cable for total of 30 hours , no joy. (also tried the same with the brand new cable)

I have tried holding the power button and the home button for a very long time (almost 5 mins) and do not see the apple logo. What happens when I try when connected to mains or USB (trying when not on charge shows me the little photo saying connect to a power supply) is the picture of a battery appears straight away, then blank screen after about 7 seconds, and then after another 7 seconds it appears again then blank screen but does not reappear again.

I can get the phone to go into DFU mode, and using Itunes (latest version) I am able to begin the recovery procedure, downloaded latest firmware 6.1.4 via itunes. The recovery process seems to be going smoothly, and get a message to say it was successful. But then the phone returns to the same state where it has a low/empty battery and will not turn on...

Any help is welcomed, I am thinking of buying a new battery from a local phone repair shop. The phone is under warranty but would really like it repaired fast so dont mind replacing the battery and voiding the warranty if this is the only possible solution...