Yes. One of the things we tried early on was to put all the remotes away in a drawer overnight, but it still happened.
Does your TV or power-management device have an old-fashioned on/off button? Is it possible that something is bumping it?
Is it possible that a momentary power glitch could cause your TV to turn on?
Have you tried disconnecting external devices from the TV to see whether the problem persists? I know you verified that none of these devices is supposed to be able to send a power-on signal, but maybe the documentation for one of them is wrong.
Have you tried temporarily taping over the IR receivers on the TV and power-management device to see whether the problem persists?
It’s pretty much got to be an IR signal causing this - as there are two different devices being affected - initially the TV, now the PowerDown device - the latter of which can only be switched on by a remote control.
There’s no sign of the problem since I taped over the lights on the router - furthermore, the sensitivity of the TV and PVR to their respective remotes seems to have improved. I think the router was just polluting the whole room with the light from its ultra-bright blue LEDs.
It still seems weird that the flashing of these lights would just coincidentally mimic the power-on signal for the TV, but I’m not sure how complex IR Remote control signal encoding actually is.
Just to eliminate all possibiliities, do you live with someone with an prankish sense of humor? There are many stories of these kind of pranks, including one about Houdini’s wife Bess learning to make a rapping sound with her toe against the footboard of their bed, and almost convincing the great skeptic of the existence of communication with the dead.
I did consider the possibility of a prank - I bet there are even annoy-a-tron type devices that do this, but no - I don’t think it’s that.
Cool. The next step is to try to trigger the problem using the router.
I dig what you’re using. However, have you ever solidly taped over the receiving eye on that device to see if the problem still occurs? If that device malfunctioned internally, couldn’t you have the same result?
I’m even wondering if some random power glitch might trigger it, because you said you had the same problem with and without the external power widget. (Unlikely, but you’ve eliminated the obvious already.)
It’s possible, but seems unlikely that two different devices would malfunction in the same way from internal causes. I only just noticed it happening with the PowerDown device though (because the TV doesn’t come on, as it would require a second hit of the remote), so haven’t had a chance to do much scenario testing
As you say, unlikely, as it would again be two different devices malfunctioning in the same way independently of one another.
This is a sound suggestion - if I move it around to the front of the TV and put some traffic through it, we’ll see what happens…
Except that since you said it happens in the early morning… I’m thinking that your network is doing a maintenance reset of some sort during that time and that is the source of the data pattern that’s causing the power on for your devices. For example, your network provider could be doing a drop/add on all devices at that time of day to reset any network updates that happened in the maintenance window (usually 1a-4a). You might call their tech support (like a real technician, not the ones reading from a decision tree) and ask if anyone has complained or if they’re dong something at that time of day.
The other thing I thought of is that you might be on a smart grid for electric and somehow the electric company equipment is accidentally cross signalling your devices during their maintenance cycle.
Maintenance cycles don’t happen every day, but they are fairly often. They are also in the early hours of the day. So they would fit the timing of your problem.
Is it possible that a momentary glitch in the electricity supply could cause this?
Do you by any chance have a UPS or filter kicking about that you could plug the TV into?
If you want it to stop, cover the IR port on your TV and see if it works.
You could try building a cone over the IR port to narrow down the direction the signal is coming from. Or, if it comes at the same time every day, you can use your phone to record a video around that time.
If you want to isolate IR signals, exposed camera film (the black parts at the start and end) works great.
Your problem doesn’t sound regular enough, but at one time I programmed my bedroom TV/cable to turn itself on at a set time in the morning as wake-up mechanism.
You can check all the menu settings and see if there is something similar.
Already done
Everytime it happens, the OP should pick up and shake a bag of cat treats, laugh, and then put away the bag. It’ll stop. 
I second this! My Big Dumb Cat would NOT come out of the neighbor’s garden last night. Treats worked! I can only presume he was playing with THEIR electronics. Bad kitty!
Um…you don’t live in SoCal, do you OP? 
Cats definitely aren’t a factor. I’ve got my eye on those gerbils, however…
That is a fantastcially evil idea! I love it!
Having deployed said deviceon a few occasions, I can attest to their craze-inducing fun. Having a small, unobtrusive device or figurine sitting on a shelf and killing the TV every now and then would be awesome.
Sounds like my sex life!
Thanks folks, I’ll be here all week.