Iphone 4 crashes when not connected to a power source

This happened to me as of 6-7 weeks ago. I thought it might have been a new app I downloaded within the preceding fortnight but even removing this didn't fix it.

It also tells me at times that there is no battery with the 'plug in screen' coming up, but when I plug it in it can have anything up to 100% battery.

When it crashes, I push the top button, the Apple logo comes up (like the turning on screen) and I can see the previous window that had been displaying at the moment of the crash still imprinted on the screen. The only thing that will ensure smooth running is when it is plugged into a power source and yet I've had the occasional crash that way too.

When not plugged in and it does run there is a constant flicker at the bottom half of the screen.

As far as I can tell it appears to be an issue with the update of ios from 7.1.1 and up (as I have since updated to 7.1.2). Is there anyway that an Apple rep could confirm or deny it? Or offer a possible solution to help fix it?