Assuming that by CPU you are referring to a separate desktop machine, you can use a crossover ethernet cable to connect them directly
Just connect the Ethernet cable (RJ-45 crossover) to the laptop .Then you will get the connection.
To connect your desktop or laptop computer to your television you will use a vga cable. Information about how to connect the devices can be found at compnetworking.about.com/od/.../a/connect-pc-tv.htm .
with a router
No, but you are going to need a wireless router, also known as an access point, between the laptop and the cable modem.
Your router should have a wireless network. Read the manual for how to enable it and set up a key, then connect to it with your laptop. Or just use a cable like with a desktop.
plug display cable on laptop with the broken screen's CPU
The computer is programmed to respond when sound cables are attached Edit: The sound cable is being attached to the laptop, but the desktop, which is in sleep mode, wakes up. The cable is not being attached to the desktop.
use a cable or install "remote desktop".
Yes. In most cases you only need a USB cable to transfer files between computers.
Yes, if you have the usb cable, you can connect it.
Step 1. Unplug ethernet wire from desktop computer. Step 2. Plug the ethernet wire you just removed into your laptop's ethernet port. Step 3. When finished browsing the internet or when portability is desired, disconnect the ethernet cable from laptop and return to the port on the desktop.