Default [Q] Broken screen impact performances?

Hi

something weird happened to me. My Note2 (TW rom + root) fell from my pocket and hit the ground, while I was driving my scooter, and I realized only a few KMs later...

After I was lucky enough to find a nice person that gave it back to me. So I was happy even if the screen was broken. The weird aspect is that since this damage, the phone is not working very well. It hangs (temporarily) and stutters, the battery is consumed more than normal, when you slide down the notification it get stuck in the middle of the screen. It is still usable and generally when you launch an app it works almost perfectly but the system is weirdly behaving. Another example is that when playing Google Music songs I have gaps.

It SEEMS that the processor is busy or has spikes of power that makes the other apps to behave slower.

So the question is: could be that a damaged screen impacts the sw behaviour (just an educated guess: maybe it's receiving lots of touch inputs due to the breaks...). If i repair the screen, will it go away?

Thanks