Brian,
Seems something similar to what I was experiencing with my OH's laptop. Kept getting the old Win 7 background and the start button would alternate between Win 7 and Win 10

Win 7 kept seeping through the Win 10 overlay.
I ended up doing a factory restore of the operating system, which put everything into a backup folder then went back to the very beginning.... 300 updates later I got the invite to upgrade to 10 back. They lied! you still get the invite after 29th! I had also created a Win 10 CD, just in case I didn't get the invite.
Anyways... I upgraded again last night from initial download to the end took about 1hr 30mins. No horrible message "This is taking longer than expected" that I got last time.
It still stuck on opening Win 10, and wouldn't let me search or get anything from the start button. Forced restarted and all is well now. I've been able to add a Microsoft account to both users accounts. Windows 7 backgrounds are no longer there. I seem to have lost/mislaid my photoshop elements CD

so that hasn't been loaded. Office and all the other programs survived the journey. I can still access all the backup folder etc., I suppose I shall have to put the printer drivers on their so that I can print via the network. That will be the next step! SIL who has Win 8 has been playing with it this morning and showing me some of the Win 8 tricks.
Whether I could have gotten out of the mess without doing a factory reset, I don't know but I got fed up with trying to sort it out and I had nothing to lose with the laptop.
THIS PC is staying WIN 7!!! I have far too much important stuff on here. It will stay that way until I buy a new pc.
It seems those who are going from Win 8 to Win 10 are having a smoother transition.