iPhone 5 Touching Itself!

Hi guys,

I purchased a used iPhone 5 the other week, and a few days later noticed that the screen had started to "touch itself". Initially this was just near the top (it kept dragging down the top menu!). When opening snapchat and using the drawing tool, it was drawing a diagonal line across the screen on its own. Also whilst typing, it would often hold down letters on its own, or the screen would freeze completely!

To get out of the frozen screen, or to stop the screen being touched down on its own I would simply turn the screen off then back on and it would be fine!... for a few secs.

My initial thought was a dodgy digitizer, so I replaced this. It worked fine for half hour then started to resume back to pressing itself!

I tried another screen, and also changed the metal back plate to the scree. Again, this would work fine for a bit then start playing up again!

Despite having 88 days warranty left, Apple wont look at it free as I've removed the screen myself... which apparently voids the warranty.

I'm stuck for ideas!

I've already tried doing a restore! Once from the phone and ones via iTunes.

Stuck for ideas, but it's really annoying! I can't even send a txt properly now without having to turn the screen off then back on a few times to avoid buttons being pressed or it pressing back to the prev screen!?

Any suggestions would be great!