Unresponsive touchscreen

I think the first thing you should do is try to restore your phone. Is it jailbroken? You may have some conflicting software on there. Also you mentioned that you recently replaced your digitizer. Maybe the part you replaced it with is malfunctioning.

 

you may have got a defective screen. I see this alot with lcd's. when you reboot they are fine and you can do all you want for as long as you want but as soon it goes into the lock screen and you unlock it again it is white. reboot and its fine. replaced the lcd and it works perfect. I have not seen this work like this on touchscreens but I guess its possible.

 

touchscreen responds only when cold

my touchscreen seems to work only when it's cold. like been in the fridge cold. but once it warms up the touchscreen stops working again.
i've restored a few times and that doesn't work.
would replacing the digitizer work?