Starting today, I have not been able to shut down my computer, it reboots every time I try.
I had a short cut that used the following command to shut down : qdbus org.kde.ksmserver /KSMServer logout 0 2 2
So, after verifying this was correct, I tried to shut down using KDE's default way of shutting down. That rebooted just like my short cut.
So, I then press my power button on my computer to shut down. That rebooted just like my short cut.
The only way I am able to shut down my computer without rebooting is to turn the power off.

This is weired. Anybody out there experiencing something like this?

Beuller....
Beuller....
Beuller....
Anybody?

After doing some updates today, the problem magically disappeared.

I know you said that it stopped now, but just in case: Are you sure it's specific to Neon?

I had that happen last year with all OSes, and a few months later the computer refused to turn on again. Hardware issue with the motherboard.

Well, the problem came back again.
I have also begun to experience other sporadic problems that lead me to think it is, as you mentioned, a motherboard issue and not a software problem.
I am going to get a newer motherboard and I will post here if the problem goes away after a month or so.