Can't login to Microsoft Account/Reset Surface RT and can't sign in to Microsoft account/Can't connect to Microsoft Services

Try this

Reset your RT from within Windows.  Reset, not refresh.  Connect the RT to charge.

https://www.microsoft.com/surface/en-us/support/warranty-service-and-recovery/refresh-or-reset-surface-rt#within

One of the pages will ask for a drive encryption key. Go to the bottom of the page and select ‘Not this Drive”

When the reset finishes, in settings go to ‘Power and Sleep’, ‘When plugged in’ set to ‘Never’

All updating is done from the Control Panel, Windows Update.

After each search for updates is complete click on the blue line that says ‘important updates are available’ to see what is found. You can speed things up by hiding all Office updates.  Right click an Office update and select ‘Hide’.    Install all other updates found. 

When Windows updates are all done and Update 3 is installed go back and restore hidden updates and install the Office Updates.

Start Update Instillation Here

Turn on WiFi, Search for updates from the Control Panel, you will see a firmware update, install all Windows updates, restart

When you go back to Windows Update it will show updates are available. Do not install these updates. What you need is KB2919355 and it will not be there.  Stay on the page and search for updates.

Install KB2919355 along with the other updates.  Restart. 

Go to Control Panel, Programs and Features, View installed updates. See that KB2919355 is installed.

Turn off  Wifi,  install KB3173424, restart

 Install KB3172614, restart

 Turn on Wifi, search for updates, should find over 200 updates, install, restart

Turn off Wi-Fi and install KB3097667

After the restart, right-click on Taskbar > Properties, Start Menu.   Check the box, Use the Start Menu instead of the Start Screen for no more metro screen. 

finish installing updates

The Microsoft image that is available to download is the same as the recovery partition on the RT if you have ever had 8.1 installed. The recovery partition never changes after you have 8.1 installed.

KB3173424, KB3172614 and KB3097667 are standalone MSI update installer files that you download to install at the correct time.

Download KB3173424 HERE.

Download KB3172614 HERE.

Download   KB3097667 Windows RT 8.1 Update 3 Standalone Package

For some reason (unless I'm not fully aware) the KB2919355 update is not showing in my update log. I've check the Microsoft website and only found the 64 bit version of the update.

I have a 32 bit OS and without this update available for my tablet, my existing Microsoft store issues still persist.

the KB2919355 update is not showing in my update log.

That would happen if you had used the WU troubleshooter.  In order to find out what you have installed you could use this PowerShell pipeline

Get-HotFix  |  sort  InstalledOn  |  ft  InstalledOn, HotFixId  -AutoSize  -Wrap

FYI

Robert Aldwinckle

Done. But Kb2919355 not in the list. Microsoft update still remain in running  (more 1 day) without news.

Thks, bye

Kb2919355 not in the list.

That tells us something about the version of your OS.   Unfortunately RT users cannot use winver the way that W10 users now do but there are clues available in PowerShell...  Even $PSVersionTable doesn't give us really current information but I bet mine is more current than yours with that one.  (I'm annoyed because I remember writing a more complete description of this exact same analysis recently but as usual Answers won't let me find it.)  Otherwise, one technique we have is using msinfo32.exe for its Loaded Modules list, sorting by Version and finding something about our maintenance that way.  For example, one module that gets updated frequently is wininet.dll.  Let's compare and see what the results imply.   Here's mine:  (I have to transcribe this because I am writing on W10 and do not have a cross-domain clipboard facility set up.)

PS C:\windows\system32> (Get-Item wininet.dll).VersionInfo.ProductVersion

11.00.9600.18538

In fact, depending on how the refresh you did is packaged, I suppose you could be completely  up-to-date and not need to have a reference to KB2919355.  But that would also depend on whether every module referenced by KB2919355 was superseded by something else and that is something that I don't know.  I also don't know how to query what update brought me that version and hence have to resort to web searches in the Support site to try to find that information.   Here is an unsuccessful attempt at doing that.

windows rt "11.00.9600.18538" site:support.microsoft.com

The problem with that will be that now they are not including File Information in the KB articles, just links to .CSV files which contain it.  This makes the lack of the DLL Help Database even more irritating.  I am going to quit this and try to calm down.

HTH

Robert