Solution to "Error Establishing Database Connection" When Updating mySQL

We just updated from mySQL version 5.1.something all the way up to mySQL 5.6. Even though we did the update in incremental steps, some of our sites went down.

It was weird, we couldn’t find any consistent trend between the sites to figure out why they went down with this mySQL database connection error.

We ended up simply updating the mySQL database password and it fixed the issue.

I share this in hopes that someone else who has this issue finds this and saves them a headache.