Hello Joel, thanks for your response.
Now, I'm trying to do what you've described. I'm trying to install update KB3145739, still it's checking for updates on my pc...it's been now for about 30 mins. For how long should I wait??
Hmmm, mine finished installing 3145739 in just about five or ten minutes. Maybe yours is having a different issue than others who found success fairly quickly.
You might want to search your system for "Installed Updates" (not Update History) and see if KB3139852 exists. Clearly that's a problem according to Microsoft Security Bulletin MS16-039.
I'm not an expert. I was simply lucky enough to come across that fix (download and install KB3145739 directly from the Microsoft website) by reading comments on the Softpedia website I referenced in my original post (15 April 2016). I was amazed it worked so quickly and others have also had great luck with it. Possibly those who were successful have similar machines.
Mine is a Sony Vaio from 2009, Upgraded OS to Windows 7 SP 1, 64bit in 2010. Replaced original HDD with 265GB SSD in 2012.