What I'm thinking is it may not have downloaded the updates correctly...of course if you backed up your "steamapps" folder you could try a clean install of the newest version.
You can either manually back them up (copy to another location, it'll take a while) or if Steam was working you could do it through Steam. Since its not, just go to Program Files (or x86) --> Steam and then find "steamapps". Now copy to another location, and uninstall Steam. Re-install and put the steamapps folder in. I THINK that should work.
I'm having this issue too, i've tried redownloading steam over and over, its not working, i've tried repairing it over and over, again its not working.
All it says for me is "updating" and once it updates it doesn't open.
* Running a virus scan, such as Malwarebytes, in Safe Mode
* Updating Windows
* Updating Steam
* In the Steam directory, delete the file ClientRegistry.blob
I deleted the file and it worked once to open, then once it froze again, it wouldnt open no matter what I did.
Try uninstalling Steam and reinstall it, but with a new directory. Instead of it creating a folder called "STEAM" in Program Files, specify the folder to be named "STEAM2".
Edit: Delete any temporary Internet files as well.