avrdude: stk500_getsync() attempt 10 of 10: not in sync: resp=0x00 So I try to compile and upload a simple code such as the Basic Blink.
I have not connected it to pin 0 or pin 1. 

There is an LED with the "L" label on the card that works. So I guess not the chip is damaged?

I have selected the correct model which is Arduino Uno / Genuino. I've checked the drivers several times now, even reinstalled Arduino Software twice and tried on 2 different computers.

5V works with ground, I can get the LED to light up. But I cannot compile / upload code.

Error MSG: avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x00
(this message repeats 10 times with attempts)


I read something about bootloader, but I have no idea how to do this / what it is. I do not have the right components for bootloading I guess. 

Also the COM is correct. I've tried using all the listed COMs without any result. Is this a hardware issue? Is my chip grilled or something?
You should re-burn the bootloader. If you have another uno, you can burn bootloader here