It still does it with no cables attached (except power).

Could it be some setting in the menus?

I reset the settings in the monitor in the menus and it still does it.

Any ideas how to fix it at all?

Typically the only reason a monitor should wake besides receiving a signal is if buttons are pressed. Are these capacitive buttons? I guess if you have anything bunched up around the monitor, sticky notes on the bezel, etc you might want to clear the area to see if anything is disturbing the buttons. Unfortunately this may be an internal sensing circuit getting tripped when it shouldn't. I have a TV that would turn on & off on its own. The fix was replacing a bad circuit board.

Bummer. This is an old monitor, but has always done it. I thought maybe it was the old PC that was doing it (z68, i3-2100T, iGPU). I had sold it several years ago and got it back recently. I added a GPU and it continued, then tried your suggestions and it still continues.

I guess I just need to power it off after use, like the previous owner did. It's so old, not sure it's worth fixing (2010).

Thanks for your help.