Click top left (it's either called file or Steam) select the Go Online option.
If that didn't help there is a more complex way too.
Go to run
type in: regedit
look for HKEY - Current User scroll to SOFTWARE
go to STEAM / Steam folder if it's an older pc it might still be Valve (was always Valve on my xp pc and you didn't list allot of info so I am just explaining in case you are on an older system)
Now look for Offline (there will be a value next to it (under "data") either 0 or 1) If it is 1 make it 0
click Ok now reboot the pc
Please note that this will cause Steam to automatically go online from now on. So if you want to go offline you will have to select go offline in the application itself.
Problem should be solved now