Had this problem all day and tried all sorts. Seems every time I connect to Steam it comes back with Network Connection error but if I retry it connects fine. Game start up fine too in online mode (inventory fine too) but no servers listed in server browser. Tried disabling firewall and AV to test but no good. Deleted ClientRegistry.blob and the other usual fixes but no good.
Found the following possible solution so trying it. Will let u know (currently repairing Steam).
Locate steam folder remove ClientRegistry.blob
when u done that u go to Control panel - uninstall a program - find Steam - Right Click And Press Repair. Takes a while.