Hi grumpgrin - it appears I have a very similar issue to what you are having. Check out the thread "Cannot Connect to the Store (Error Code 0x80072ee2). in the Windows 8.1 forum. Are you still having this issue? If not, did you do anything to fix it? Thank you!
Hello GRBU2,
Hope you have sorted things for yourself.
At one point everything was fine and I could get into "my account" and "my apps" list with no problem. Then it went belly up again.
However, I am not finding it a problem as I don't really need to access the "my apps" list or "my account" (Windows Store not Microsoft). I have no issues accessing the Store itself or searching and installing apps if needed. All apps I use at the current time are working fine. I did have issue with the Mail app. It was not updating email (although People and Calandar were working fine. I just uninstalled and re-installed the app and it is working fine now.
There are no updates outstanding. I did try and contact Microsoft support for live chat but alas that is as bad as trying to load "my account" and "my apps". It just tells me that there has been an error and try again blah blah. I don't want to use the call back support and even if I did/could access it there were far too many people waiting in line (over 50 and that was minutes before closing time last night!).
Anyway, it's just these few Microsoft things that are not working at their best and they are not essential for my needs at the moment.
Regards to you.