I've had weird problems like that before. Try re-installing Steam over the old install. Not sure if you need to back-up any save files, but I don't think you will.
Also check firewalls. Some will block programs that have been modified recently, such as by an update, or may be stopping the update for some other reason.
...Oh, and before anything, try killing Steam.exe in the task manager first, then starting it from its icon. Steam.exe is notorious for having hangups, freezes, and slowdowns after running for a long time.