Update: My solution was to disable all plugins (I had to do it by moving them out of the plugins folder manually), then I was able to log in. I re-enabled plugins one by one after upgrading, but it seems things are working now even with most of the plugins back. Give that a shot if you’re still having problems.
This solved my issue too. Try it if you haven’t.
Upgrading to 2.6.2 is the worst experience I’ve had this week.
