Many find after applying a CF update that either CF won't start at all, or they can't access the CF Admin, or some part of CF or their app doesn't work. The problem may be simply that there was an error in the update process CF did, and it may be rather easily confirmed and resolved.
In this post, I share several tips and observations to help resolve this, based on my years of providing remote CF troubleshooting support.
The TLDR version: check the CF update log, and if there are errors, try stopping CF yourself and manually apply the update from the command line. If that's enough to get you going, great--especially if you ARE in panic mode! (If the "problem" you need to solve, instead, is that you can't get CF to show you updates because you're behind a firewall preventing outbound internet access, I help with that also, toward the end.)
For most people, though, even those "simple things to do" can prove challenging (and understandably so). And you may find different resources on the web offering perhaps truncated discussions of the topics, which is why I elaborate on things in this post.
And even if you're in a panic, it may take only about 10 minutes to read this whole post. (You can also hire me to help instead, of course. See the link above.) Hope the info to follow is helpful for you.