Go on line,log in to Steam and try playing on line for a while......now bring up the Task Manager by pressing Cont/Alt/Delete and end Steam from the appications tab.Close Task manager and reopen HalfLife from the taskbar.
You should be able to carry on playing off line now.
I think that Steam needs to reverify all the files on line from time to time.
With a bit of luck you should be able to start the game in off line mode again after this.
Coming back too this problem I backed up my save games so I opened up Stream in the main area and clicked on Harlf Life and Properties and local options and back up saved game files in which I did and saved on to a DVD-RW Disk. So when I restored the game file I had no save games present what do I do ?