Definitely not mouse activity.   This happens with no one in the room. This actually isn't unique.  If you google it you will see others have had the problem.  i think it is something in windows 10.  I have tried a few things with the network card settings.  but the computer is not wired now and as far as I know this mother board does not have wifi.  i will look in the bios

Check the task scheduler to see if it's waking up Windows for assorted things like update checks, mail collection, backups, virus scans etc. Also check things like Acrobat, anti-virus and anything else that might be set to regularly check for updates to itself. Checking if it's set to "wake on LAN" might also turn up something - sometimes routers or something else on the LAN sends out a bunch of "who's around?" queries, tries to update it's network resources status or allocate new DCHP addresses, and a computer set to wake on LAN can sometimes kick into life because of them.

I'm assuming the PC is actually asleep, rather than shut down and switched off. If it is really off, with the switch on the back of the PSU in the off position or power switched off at the wall socket I suggest you contact your local religious leader of choice and enquire about their services regarding the removal of unwanted apparitions.

The power supply is not turned off
 

HighAndDry
The power supply is not turned off

As tlw commented, it does sound like it's asleep rather than shut down.
 
Check the system log to make sure it's actually shutting down.  If it is, then try this: Next time you shut down, power off the PS, then hold down the case power button for a few seconds.  This will drain the caps (capacitors) of any residual power.
 
If that solves the problem, you could have bad caps on the motherboard.

On Win10, I am not sure of specifics in the O/S, but just ran through my BIOS quick to give you better feedback. In my BIOS there is a dumbed-down first screen and need to "Exit/Advanced" to shift into Advanced Mode. This gives you access to the full UI. From there, there is also an "Advanced" tab at the top, and at the bottom of the list is "APM." Clicking that shows the following list for me:
 
Restore AC Power Loss
Power on by PS/2 Keyboard
Power on by PS/2 Mouse
Power on by PCI
Power on by PCIE
Power on by Ring
Power on by RTC
 
Your BIOS may be laid out differently, but those are essentially what you are looking for. I have all of the "Power on by..." options disabled.
 
Please note: even if you are the only one to use your machine it is highly recommended to require a login to start Windows. Additionally, disabling "Remote Assistance" (in the O/S) is also highly recommended - if you ever do need this you can always enable it.
 
Having a static IP is another reason to disable the above if you are hard-wired to the internet. Anyone with your IP address can enable Remote Desktop and send a wake-up to your computer (this is the wake-on-LAN, which is "Power on by PCI"). If you do not have a password to start windows/remote assistance off, someone can potentially gain access to your machine this way.
 
Again, I am not sure of Win10 specifics or of your BIOS, but the above items are ones to check.

mettelus
Having a static IP is another reason to disable the above if you are hard-wired to the internet. Anyone with your IP address can enable Remote Desktop and send a wake-up to your computer (this is the wake-on-LAN, which is "Power on by PCI"). If you do not have a password to start windows/remote assistance off, someone can potentially gain access to your machine this way.
 

Wake on LAN uses the MAC address not the IP address and is generally not something that can be used over a WAN.
 
 
And again, the powercfg command I linked instructions to above will tell one exactly what caused Windows to wake up.

One thing to consider is a brief power glitch that happens while the computer is unattended. The computer is never really off, in the sense that the power supply is constantly applying a bias to the mainboard except when it is unplugged or the switch on the power supply is open. In addition if Windows has not been altered from default fast boot, Win 10 will not even fully restart from a shutdown. 
 
In any event you should look in your BIOS for a setting on how the machine is to restore from AC power loss. A brief drop and return to nominal in line voltage may trigger a boot sequence if that is set to 'always on' or 'last state'. You BIOS may describe those events with different language. 
 
In fact your board has only two settings. From the manual:
"Restore on AC/Power Loss
Select the power state after a power failure. If [Power Off] is selected, the power will
remain off when the power recovers. If [Power On] is selected, the system will start
to boot up when the power recovers."
 

You could eliminate some possible causes by disconnecting a few things one at a time. When you are leaving the computer off for a while, disconnect the ethernet cable. If it still comes on, then you know it's not a network trigger. Next try leaving the mouse disconnected, then the keyboard.

Just a thought. If the mouse or keyboard is wireless, maybe the usb receiver is picking up a stray signal.

Also wondering, do you have a cat?

Kev999
Also wondering, do you have a cat?

Or children, for that matter.  A DAW user in another forum was experiencing the same problem, and it turned out his young kids were starting up the PC when he wasn't there.

Since it's a new build I would go back in and check the install. Double check everything and make sure there isn't a tiny screw or something that is shorting the MB to the case or rolling around on the MB. Triple check the connection to the power button. It could be a problem related to vibration that mimics a person pressing the power button.