After completing my screen replacement due to it being severely shattered, I was not able to get the iphone to boot up....

The whole touchscreen on phone is non responsive? Well you can start by tearing down the phone and check the connections for the digitizer, if No issue with connection then you may need to replace the touch screen

if an iphone check if the SMS message/ iMessage is "active" or "on" sometimes it is found OFF

Since the fan is ON, that is a good sign that the motherboard is working. On the laptop there should be an indicator of an object shaped like a can, does it appear to be blinking? Was the laptop ever dropped/slammed shut after the last time it was used? Try: Turn On laptop and let it boot up (I know you cant tell if it is on or not but give it few minutes then... Hold down one of the keys on the keyboard for at least 30 seconds you should get a response sound, that should indicate that the computer is on but now may be the back light of the LCD. If you have a flash light shine it at the screen from the sides to see if you can see any images on. This can help determine if the back light failed.