after the new software update two of my Apple TVs stopped working and refuse to reboot

If you see a warning symbol on Apple TV - Apple Support

If you have an Apple TV 4K

If you see a […] flashing indicator light on the front of your Apple TV, contact Apple Support. 

A continuously flashing status light may be an error that requires assistance from Apple. Please contact them.

I'm having this problem, too. I have 2 Apple TVs - a Apple TV 4K (1st generation) and a Apple TV HD. Both have a flashing white light. The 4K gave me the image with the TV and the iPhone, but after I entered the code, it attempted to reboot and hasn't displayed anything since. Now both have blinking white lights and nothing on the display. I've plugged the HD one into my laptop, since it has a port, and am attempting to reinstall the software from there. It sounds like I'll have to take the 4K into the shop. But I'd like to understand why BOTH my devices went out at the same time.

… and they rebooted but still do not work

Exactly what doesn’t work?

Do you get the Home Screen with the various apps?

If you go to Settings﹥Network﹥, does it show the device to be internet connected?

Can you launch apps? Apple apps and third party apps? Do you see content?

Can you start any media, in any app?

Do you get error messages? What do they say exactly?