How do I restore Word as my file editor? Office 365 killed it.

I poked around the forum a bit and found some old dead threads, not fully answered, so i am posting for help!
I recently subscribed to Office 365 (that and the usual Microsoft updates are all that have changed on my computer in the last week) but now Windows Word (Office 2010 local installation) is no longer my default editor.

I tried the default programs utility, but it does not even know that Office 2010 is still installed. I can run Word manually, browse and open a file. I can browse to a file and Open With to get to Word, but by default, DOCx files want to open with wordpad of all things!

How can I get this reconfigured. I would NOT like to have to reinstall office.

RECAP FOR THIS THREAD (for members finding this same problem)
There is some root cause problem yet undetermined with the assignment of default programs.
An error message appears where a list of programs should appear.
The root problem affects other types of file associations too, this problem is not limited to office.
Re-registering Microsoft Office (i.e. winword /r) had a positive effect on being able to click an office file to open it, but none of the office programs appear available as a select-able default.

Right-click "open with" > "set default program" still results in an error message. (MOVING THIS ASPECT TO ANOTHER THREAD.)

Do you have Office 2010 installed ?

Browse to a word file with the docx extension then right-click and select "Open with ..." then click on "Choose default program...". On the Open with dialog, put a checkmark in the box that says "Always use the selected program to open this kind of file" and then click on browse. Navigate to where Word is installed, should be someplace like C:\Program Files\Microsoft Office\Office 14 and find the file winword.exe, click on it then click Open. That dialog will close, click OK on the remaining dialog and you should be good to go.