Today I noticed the UPGRADE (to 3.4.1) button in the admin area of my site, so I clicked it. Mistake. I lost access to the admin area.
My site is hosted at Godaddy. So... a few hours later, I logged onto the Godaddy site, and went to the MANAGE APPLICATIONS area. There was another UPGRADE (to 3.4.1) button there, at Godaddy. So I clicked that, followed the instructions to choose an upgrade time, and soon everything was fine. I can get to my admin area again, and I am now running 3.4.1.
For me, the UPGRADE button within my admin area of my site DID NOT WORK. Telling my hosting service (Godaddy) to upgrade WORKED, (even after the problem with the UPGRADE button on my site).