I am connected to cable internet, When i shut off my computer am I still vunalrble to hackers? Am I still conncted to the internet even though my computer is off?

"Am I still conncted to the internet even though my computer is off?"

No. With the machine off, nothing is running. It's like a lamp that is off. It's plugged in, but nothing gets to the lightbulb to illuminate it with the switch off.