Screen not working due to damaged home button cable?

A girl smashed my iPhone 5s a few months ago, luckily it had a case on it. However, my screen popped off completely, it did not crack or break. All ribbon cables for the display are in tact and while investigating at times it would light up and but 99% of the time it wouldn't. Now after it happened the phone was still powered on, I could hear it ringing, I even activated Voice over somehow. Now the problem I am running into is there is a broken cable. I thought it was the home button cable however after I removed the cover I see a nice looking copper ribbon cable running from it to a small computer chip right beside it. THIS is where things are broken. There is a little piece of a ribbon cable leading from the bottom of this chip that is snapped off and I have a cable that is about an inch and a half long, very thin just like a ribbon cable, has a QR code printed on one side, underneath that QR code it looks like another little chip that connects to the chip next to the home button. The other end snaps has a little connector that snaps into a little piece right underneath the battery and above the charger. That cable is completely ruined I believe since it cannot connect to the chip that is next to the home button where the ribbon cable runs to from the home button.

*EDIT* I figured out that this is the actual home button flex cable. So now my concern is could this cable prevent my screen from working. And a recent revelation since this phone has been sitting for months as is; I plugged in a charger and it has been on the charger for over a half hour and I cannot start the phone. I used to get a vibrate or some sort of activity, now I'm getting nothing. Like I said before all cables are in tact and regardless if the 3 screen cables were broken that shouldn't stop the phone from turning on should it? This is everything I have done. I have taken the phone apart 4 times since then. I did a hard reset and actually upgraded it from 7.1.2 to 7.1.4 I believe. I have inspected cable after cable after cable, I have checked to make sure the screen seats back down in it's housing perfectly so that literally the phone looks like it's in mint condition, I have investigated literally everything I know in order to figure this out and now I plug it in the computer and I get no sign of it being detected, I'm getting no vibration, I'm getting nothing. It may be a cable or it may not be, I just took it apart just now to make sure I had all my facts straight for this post since I hadn't worked on it for such a long time.

I need to know, would the broken home button cable from the chip alongside the home button prevent the screen from working? I need to fix this phone, I have fixed hundreds of iPhones since the first generation and this is the 1st iPhone 5s and unfortunately it is mine because some unstable girl got upset and decided to spike it like a football and got away with it without any punishment whatsoever, no fine no jail time, no restitution, nothing. So I am very upset. If I can fix this thing myself with a few parts and you know or are at least 75% sure you know what parts I need to get it up and running for 10-20 dollars I would love your input. If I have to take it to a repair person I am going to have to sell it because I cannot afford to pay $200 for a $5 part and 20 minutes of a guy's time. Please help me out here! I can provide photos sometime if needed but I really prefer not to take this thing apart again unless it is replacing parts and getting it working. Thank you.