My iPhone 5C's screen has turned blue during restore.

The other day my iPhone 5c started switching off & on again for no reason, it started getting worse as it would start to switch on then switch off again and took about 5 attempts to switch on. This got progressively worse until yesterday it finally gave up the ghost and refused to switch on. I spoke to my service provider (O2) via the live chat feature and was instructed to press the top and home buttons at the same time. I did this and the screen then showed a pic of a cable pointing to the iTunes logo, so I connected it to iTunes and it said I needed to update my IOS, so I tried that and it just kept getting so far before a message would appear saying it couldn't complete the task "for an unknown reason". So this morning I took it to the Apple store and got a walk in appointment with one of their genius' who proceeded to attempt the same thing over and over with the same results. He said he didn't want to do a restore in the shop as I could do it at home and restore backup at the same time. I have tried over and over to restore the phone and I just keep getting the same message as I got when I tried to update it. Now while attempting it for the last time tonight, the screen has now turned blue with horizontal red, white and black lines covering the top inch of the screen and iTunes just says "Restoring iPhone software..." but makes no actual progress. I am at a loss as to what's happened as the phone has never been damaged, water damaged, jailbroken or hacked.

Any help, tips or advice would be very gratefully received.

Thanks.