Why is screen working on its own?

Basically, I bought a second hand iPhone 6, and when i first got it i noticed a few letters on the keyboard would press themselves, this progessively got worse to the point where i couldn't use the phone as it would just glitch out and have control of the screen. I ended up replacing the screen and yet it was the same when i powered the phone up. I decided to remove the lcd shield and turn the phone on with assistive touch and to my surprise the screen seemed to beworking fine. This is when i realised i hadn't removed the purple sticker on the back of the new screen. thinking it must be that, i put everything back together. To my dissapointment, the problem persisted. Could it be a faulty screen, the lcd shield is somehow messing with the screen or something else entirely?

Hopefully someone out there has a solution because im really dissapointed at the moment.