How bad is my screen damaged? Do I need to replace the whole screen?

Question

My dad has a Samsung phone. He dropped it once long ago and there was a crack across the screen as shown in the image:

Now he is having difficulty using the phone. There is always a touch at one spot automatically, which is very annoying. To show you what I mean, I have enabled "Show touch" in "Developer Options".

I have uploaded a video on youtube here showing how annoying it is.

Here are images showing the unwanted touch:

So how bad is the screen damaged? Do I need to replace the whole screen, as the guy at the repair shop said?

Update:

Answer 1

If there's a constant "touch" at one spot, the digitizer is probably damaged, along with the glass. For some screen cracks, it's possible to replace the glass only (at least in some Samsung models including the Galaxy S4, which yours appears to be). Unfortunately, that's probably not the case here. A complete screen and digitizer assembly and labor to replace it cost about as much as a good used phone of that model, or a bit more than the insurance deductible if you carry insurance with service. If you can do the work yourself, cost would be reduced by about 1/3, and it may be worth attempting.