Windows 10 Start menu>Power, Settings or Action Center menus open for 1 second and close.

I have seen a bit of this here. No issue on my own Windows 10 machines (3) or any client machine that I am aware of.

Given what you have done, try the following:

1. Update BIOS, Chipset, Video and Power Management drivers.
2. Do a Windows 10 Repair Install and keep everything. Make sure you follow closely and nothing will be lost. I have done this numerous times.

Go to the Media Creation Link

https://www.microsoft.com/en-us/software-download/windows10

Windows 10 is running, so click on the Download button (not Upgrade Button, select Open (Run) but NOT Save. Allow the program to run. Allow drivers to update. Then select Keep Everything

Create a new local Administrator user account, switch into it and test the issue.

Not to be flip but been there done that. I've been troubleshooting this for a while and read many of the suggestions to try along with the advice to update drivers and system files etc. The alternate Administrator creation I had hoped would work because that would at least isolate the problem to a profile, but alas that was not to be. I've been doing this for a long time too and this is starting to look like a nuke & rebuild type of problem. I just keep hoping someone knows which Microsoft Update or some other pushed update is the lone culprit.

If you have done the two steps (large ones) I suggested and no result, then take one problem machine and do a fresh install of Windows 10. Update all Windows and Drivers before adding anything and then add software carefully testing as you go. You may find some conflicting software.

Did you check it in Safe Mode ?

I am hesitant to pour salt on the wound by installing Windows 10 over the existing copy since these operations are always a gamble. Nevertheless I'm creating a copy of the media to USB from the media creation tool. I had done a "Reset" already via a Shift + Restart and then a "Keep Files" which yielded zip. Ramin - I did run it in "Safe Mode" & tested for the closing window problem and it was exactly the same behaviour as Normal Mode. I also tried to run antivirus and MalwareBytes in Safe Mode but it would not. I did run an antivirus check with Avast at startup mode which kicks off before the OS fully loads for those hard to see buggers.

You apparently have software conflicting with Windows 10 and I suggest taking one machine as test, building it up from scratch and then determine what the issue is. Initially depend upon Windows Defender instead of Avast  and see. Windows Defender is excellent.

I only have one machine. It's my home PC that has multiple (expensive) music creation software that have been working perfectly for years. In fact this problem just arrived out of the blue recently. I haven't installed anything new and all the software played nicely together. That's why my money's on either malware or a Windows Update. I do normally rely on Windows Defender but it would not run in safe mode, has no pre-OS mode to load before services.

I now have the latest & greatest Windows 10 after a new repair install. And my original problem; "Action Center menus open for 1 second and close." still exists. Same problem with the Start menu as well. All those items open briefly & quickly close. I did read somewhere that it was suggested that, for the Action Menu, to try using both mouse buttons on the Action Menu icon. The trick being to press the left button first but both buttons almost simultaneously. That actually works -but only for the Action Menu.
Maybe a month from now someone stumbles upon this question and knows the answer. As far as typical troubleshooting goes, there ain't much left to do. I do appreciate the help though, thanks guys.

Can you try a different USB mouse that is a real mouse to see if that helps?

What you describe is not an issue on any of our client (or my own) Windows 10 computers. Try an external mouse to see.

I suspected perhaps Keyboard or mouse drivers might have become problematic. uninstalled both. Tried a PS2 mouse. Executed the get-appxpackage | remove-appxpackage command in PowerShell. No changes to the original problem.

Will you give feedback on the rest of the suggestions, please?

I created a fresh user. Elevated to Admin. restarted as new user with no changes to original problem. As far as installing Classic Shell, that is just polishing a turd. I want to know what is causing this problem regardless whether it can be corrected or not. If there is no way to return the OS to a correctly functioning state, I want to know. That the only viable solution is to nuke the current environment and do a clean reinstall of the OS. Not really in a hurry at this point. Another angle was the possibility that a Microsoft Update is the culprit. I rolled back any pushed updates for 2017. That yielded nothing as far as a resolution. As I mentioned earlier, pressing both buttons on the mouse to open the Action Center menu seems to work well enough but it's still a kludge.

Yes, I'm afraid it's goose eggs for this one. Like I said maybe someday, someone will happen upon this and say Hey, wait a minute I had that same exact problem and you know what fixed it? All I had to do was tweak this key in regedit.
HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\secret\FixAllAnnoyingBehavior

Very interesting!

There was nothing to indicate the action taken would result in solving the problem. The solution was more of a side effect of actions taken to remove all software to rebuild the environment.