KB 2871389 not applicable to my system makes 8.1 impossible to install???

In most cases, the only time you would receive the error message that KB 2871389 is not applicable to your system would be if your system is managed by an administrator and/or Microsoft Windows Intune as Windows Intune classifies this install as "Not Applicable".   The work around is to click the Window key and type Windows Update.  Once you've typed that, select the option that says Install Optional Updates.  Once there, click on the blue hyperlink that says Check online for updates from Microsoft Update.  This will override the normal automatic updates and/or Windows Intune from determining that this update is "Not Applicable".  Install the important updates that are listed only.  Once complete, revisit the Windows Store and your free upgrade option should now appear as the first big block on the left.

Nope, that didn't work.

Have you run the Windows 8.1 Upgrade Assistant?  If you've already done that without success, attempt a Refresh of your PC.  This will not affect any of your personal files.  To do so, move your mouse to the bottom right corner of the screen, when the transparent icons appear, click on the Settings tool, then at the bottom right of the screen on the Settings window which appears, click the Change PC settings link, then click on the General tab to the middle left, scroll down on the right and click on the Get started button under "Refresh your PC without affecting your files".  Follow the prompts to complete the process.  Once you've completed the refresh, revisit the Windows update exactly as described in the last suggestion.  The reason we say this is due to the fact that if you were to access the Windows Update "App", through Settings, clicking Windows update on the left and then clicking on the Check for updates now button, it wouldn't give you the option for the required update.  However, if done through the alternate method, thus far a 90% fix.  Once completed, attempt to go to the Windows Store and look for the tile which will appear immediately upon entering the store, inviting you to upgrade to Windows 8.1 for free.  If this doesn't fix the challenge, please describe in detail your efforts in getting you to the point you were prior to contacting the community for support.  

I am facing exactly the same problems that you are... 
haven't found any workaround till now.

Have you run the Windows 8.1 Upgrade Assistant?  If you've already done that without success, attempt a Refresh of your PC.  This will not affect any of your personal files.  To do so, move your mouse to the bottom right corner of the screen, when the transparent icons appear, click on the Settings tool, then at the bottom right of the screen on the Settings window which appears, click the Change PC settings link, then click on the General tab to the middle left, scroll down on the right and click on the Get started button under "Refresh your PC without affecting your files".  Follow the prompts to complete the process.  Once you've completed the refresh, revisit the Windows update exactly as described in the last suggestion.  The reason we say this is due to the fact that if you were to access the Windows Update "App", through Settings, clicking Windows update on the left and then clicking on the Check for updates now button, it wouldn't give you the option for the required update.  However, if done through the alternate method, thus far a 90% fix.  Once completed, attempt to go to the Windows Store and look for the tile which will appear immediately upon entering the store, inviting you to upgrade to Windows 8.1 for free.  If this doesn't fix the challenge, please describe in detail your efforts in getting you to the point you were prior to contacting the community for support.  

DO NOT FOLLOW THESE DIRECTIONS:  If you "Refresh your PC without affecting your files" it will remove any programs you either downloaded from the Internet or a disk. Yes, it will keep your photos and music, but you can kiss Word, etc., goodbye. Oh, just to be nice, the refresh option leaves you a list of programs it removed. Hence, you can gather all your disks together and reload them on your harddrive.

INFORMATION REGARDS TO THIS POSTING AND NOT FOLLOWING THESE DIRECTIONS WOULD ADVERTLY DENY TECHNICAL SUPPORT FOR ANY ISSUE WHICH THIS IN FACT RESOLVES.  KEEP IN MIND THAT THIS FIX IS A LAST RESORT EFFORT!  THIS SHOULD NOT BE ATTEMPTED WITHOUT FIRST ATTEMPTING THE WORK AROUND DESCRIBED PREVIOUS TO ANY REFRESHING OF THE PC.

TO THOSE WHICH THE FIX DESCRIBED AT FIRST (MINUS THE REFRESH OF YOUR PC PART), THIS IS A 90% FIX.  IF YOU'RE STILL EXPERIENCING ISSUES WITH THIS INSTALLATION AFTER THE ATTEMPT DESCRIBED, PLEASE ESCALATE THIS ISSUE TO MICROSOFT SUPPORT.  SHOULD THERE BE ANOTHER WORK AROUND FOUND, WE WILL POST IT.

ALSO NOTE:   REFRESHING YOUR PC CAN REMOVE THIRD PARTY SOFTWARE APPLICATIONS, SO PROVIDED THE COPIES OF YOUR SOFTWARE ARE LEGAL AND YOU HAVE THE PRODUCT KEYS AND OR ACTIVATION SEQUENCE / SERIAL NUMBERS, YOU WILL BE FINE.  YOUR FILES FOR EACH OF THESE PROGRAMS WILL NOT BE AFFECTED, NOR WILL YOUR PHOTOS AND MUSIC.

Attempted to refresh, but that was met with failure. Windows 8 will not refresh. The problems keep mounting.

I was facing the same problem.. 
try reset ..after taking a backup of your important files..

Same here with frustration. KB patch not installable, refresh not statrted! The only option now is fresh installation?