Something that just hit me, because it's been discussed over the last day on another group I haunt, is that you could be encountering this issue because Fast Start is enabled (and has been, by default, since Windows 8 - there's nothing 10 specific about this at all).
When Fast Start is on when you use "Shut Down" to do what you think would be a complete shutdown of the computer it doesn't really shut down, but instead goes into a specialized form of hibernation. When it's turned on again it does not boot from scratch but instead reads the hiberfile, and the usual early boot steps do not take place.
You can get around this in one of two ways. You can turn off Fast Start by going to the Power Settings, "Change what the Power Button does," link and when that dialog opens there will be a link at the top that says something like, "Enable options that are not currently available," which, when clicked, will cause all the checkboxes that are stippled out at the bottom of the dialog, including the one for Fast Start, to become accessible. Uncheck it and then when you shut down you actually shut all the way down.
Another option, if you prefer to keep Fast Start enabled, is to do a Restart. Oddly enough (to me, anyway) Restart does a full shutdown and automatically restarts the computer which then loads everything from scratch. If you start hitting your UEFI invocation key after the screen goes black and keep hitting it about once per second as the restart proceeds you'll get your UEFI menu screen.
Of course it won't boot using optical media or bootable USB because in order to tell it to do this you must first access the BIOS options, which look pretty much just like they always did, via your UEFI menu. You're in a catch 22 because things changed post Win7 and you've not gone down this path (yet) for the first time. There is nothing so constant as change.
Edited by britechguy, 21 May 2016 - 07:50 PM.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1809, Build 17763
Travel is fatal to prejudice, bigotry, and narrow-mindedness, and many of our people need it sorely on these accounts. Broad, wholesome, charitable views of men and things cannot be acquired by vegetating in one little corner of the earth all one's lifetime.
~ Mark Twain