PC looses connection to the internet at times

Do you have the "Hibernate" function in use?

I know, theoretically, that this should not be an issue unless the computer is actually in hibernation, but, I recently had the same problem on one of my laptops. I tried many different options. It eventually occurred to me that the problem had started after staring to experiment with the hibernate facility. I turned it off and the problem was solved. But I am not optimistic in your case. I think this was Bios related, which would vary computer to computer.
Fwiw. The message for the Lan is not associated with this problem.Do you actually have a LAN? It seems that the computer is loking for a second connection. Look in the device manager at the network adapters and see what you have there.

Hibernate is turned off as far as I can tell. I went to Power Options - advanced Setttings - Sleep - Hibernate after - Setting: Never.

Is there another way to check?

I'm not on a LAN, I just have my own PC. When I installed Windows, I let it setup a Homegroup.

I attached two screen shots of my Network from the Advanced and Driver tabs, in case this might help. Maybe one of the settings on the Advanced tab could be changed. I