Many people recommend running memtest overnight before concluding that the memory is good. I think 2+ hours is enough to conclude that the memory is likely good though.

In your first post you said this problem started after a software update. Do you remember what software was updated when this problem developed?
Do you have any ppa repos, or other 3rd party repos in your sources.list? If so, you might consider leaving them out when you reinstall Ubuntu. The quality of those ppa and other 3rd party repos varies widely. Many are fine; but many others have caused a lot of people dependency nightmares and other problems.
If the memory and the hard drive are not faulty, then obviously some software got screwed up somewhere along the line. Third party repos would be the most likely culprit here. Sorry I don't have a more definitive answer for you.