I had this error message when trying to log onto Steam today. I left it a couple of hours but it still wouldn’t let me log on.
Cannot Connect to Steam Network – please try again later.
What you may need to do, which worked for me is to delete ‘ClientRegistry.blob’ in Steam’s installation folder (C:\Program Files\Steam) and try to restart steam. If this doesn’t do the trick try deleting ‘AppUpdateStats.blob‘.
I also had to run Steam with administrator privileges initially after this to get it to work, let me know if this works for you too.